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18jonea
 one year ago
Add/Subtract: : Simplify and state the domain.
18jonea
 one year ago
Add/Subtract: : Simplify and state the domain.

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1can't really understand this? what is going on with that 1/4 over there... And I see you have  + in between the first two fractions.

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0the plus is suppose to be over before the 1/4

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{7}{x+6}\frac{x+2}{2x+2}+\frac{1}{4}?\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well first 2x+2 can be written as 2(x+1) \[\frac{7}{x+6}\frac{x+2}{2(x+1)}+\frac{1}{4}\] now look at the bottoms of all the fractions and ask yourself how you can find a common denominator

freckles
 one year ago
Best ResponseYou've already chosen the best response.1what does that mean exactly

freckles
 one year ago
Best ResponseYou've already chosen the best response.1"no?" I don't understand the response to what I said.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1does that mean you don't know how to find a common denominator ?

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0i dont know how to find the common denominator

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well if you notice the denominators are x+6 and 2(x+1) and 4

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so a common denominator could be (x+6)*(x+1)*4

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the first fraction... \[\frac{7}{x+6}\] how can we write this as something over/[4(x+6)(x+1)]?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1notice on bottom it is lacking the 4 and the (x+1) so just multiply both top and bottom by 4(x+1) that is how you can get this new bottom we speak of ... \[\frac{7}{x+6} \\ \text{ multiply top and bottom by } 4(x+1) \\ \frac{7}{x+6} \cdot \frac{4(x+1)}{4(x+1)}=\frac{7 \cdot 4(x+1)}{4(x+6)(x+1)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1now look at the second fraction

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{x+2}{2(x+1)}\] remember we want 4(x+6)(x+1) on bottom so what is this bottom lacking in order to get that?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and also 2 right since 2*2=4

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{x+2}{2(x+1)} \cdot \frac{2(x+6)}{2(x+6)} =\frac{2(x+2)(x+6)}{2 \cdot 2 (x+6)(x+1)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we wanted 4(x+1)(x+6) on bottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we had 2(x+1) on bottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.12(x+1)*what=4(x+1)(x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1divide both sides 2(x+1) \[what=\frac{4(x+1)(x+6)}{2(x+1)}=\frac{4}{2} \frac{(x+1)}{(x+1)} \frac{x+6}{1} \\ what=2 (1)(x+6) \\ what=2(x+6)\] so 2(x+1)*2(x+6)=4(x+1)(x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so what we needed to do to get the bottom 4(x+1)(x+6) for the second fraction was multiply the second fraction on top and bottom by 2(x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so far we have: \[\frac{7}{x+6}\frac{x+2}{2(x+1)}+\frac{1}{4} \\ = \\ \frac{7 \cdot 4(x+1)}{4(x+6)(x+1)}\frac{2(x+6)(x+2)}{4(x+1)(x+6)}+\frac{1}{4} \\ \text{ so we are already able to combine the first two fractions } \\ \frac{7 \cdot 4(x+1)2(x+6)(x+2)}{4(x+1)(x+6)}+\frac{1}{4}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you still need to do the same thing you did to the first two fractions to the third

freckles
 one year ago
Best ResponseYou've already chosen the best response.1what do we need to multiply 4 by so that we have 4(x+1)(x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1right so multiply top and bottom by (x+1)(x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{4}=\frac{1(x+1)(x+6)}{4(x+1)(x+6)} \text{ or just } =\frac{(x+1)(x+6)}{4(x+1)(x+6)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so this gives us: \[\frac{7}{x+6}\frac{x+2}{2(x+1)}+\frac{1}{4} \\ = \\ \frac{7 \cdot 4(x+1)}{4(x+6)(x+1)}\frac{2(x+6)(x+2)}{4(x+1)(x+6)}+\frac{1}{4} \\ \text{ so we are already able to combine the first two fractions } \\ \frac{7 \cdot 4(x+1)2(x+6)(x+2)}{4(x+1)(x+6)}+\frac{1}{4}\] \[\frac{7 \cdot 4(x+1)2(x+6)(x+2)+(x+1)(x+6)}{4(x+1)(x+6)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you should multiply everything out on top and combine any like terms

freckles
 one year ago
Best ResponseYou've already chosen the best response.1also notice the domain can be found from the start

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you don't want any of the fractions to be 0 on bottom so to find the domain say all real numbers except x+1=0 or x+6=0 (I will let you solve those equations)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the second fraction had x+2 in the numerator

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and the second fraction also had 2x+2 on bottom 2x+2=2(x+1)

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0is the domain all real numbers except when x = 6 or 1

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0wait it would be 6 right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.16 is right 1 is incorrect this is because 1+1=0 isn't a true equation

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the domain is all real numbers except x=1 or x=6

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0right i just figured that out

freckles
 one year ago
Best ResponseYou've already chosen the best response.1did you ever try multiplying the top and combining like terms yet?

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0i am trying to figure out the second equation you did... can you show me how you did it again please

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0yes the second fraction

freckles
 one year ago
Best ResponseYou've already chosen the best response.1this was the second fraction \[\frac{x+2}{2(x+1)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we wanted the bottom to be 4(x+1)(x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the bottom is missing factors 2 and (x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so we multiply top and bottom by 2(x+6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{x+2}{2(x+1)} \cdot \frac{2(x+6)}{2(x+6)} \\ =\frac{2(x+2)(x+6)}{2 \cdot 2(x+1)(x+6)} \\ = \frac{2(x+2)(x+6)}{4(x+1)(x+6)}\]

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0ok i am goimg to try and multiply now

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0yeah i have no idea how to even start... can you help

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0wouldnt the second one be 2x squared +16x + 24

freckles
 one year ago
Best ResponseYou've already chosen the best response.12(x+2)(x+6) = 2(x^2+6x+2x+12) 2(x^2+8x+12) 2x^2+16x+24 is right and then there is a negative in front of that mess 2(x+2)(x+6) so it is actually 2x^216x24

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{7 \cdot 4(x+1)2(x+6)(x+2)+(x+1)(x+6)}{4(x+1)(x+6)} \\ \frac{28(x+1)2x^216x24+(x+1)(x+6)}{4(x+1)(x+6)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.128(x+1)=28x+28 and (x+1)(x+6)=x^2+6x+1x+6 (x+1)(x+6)+x^2+7x+6

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{28x+282x^216x24+x^2+7x+6}{4(x+1)(x+6)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1combine like terms on top

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0to combine all of them i got x^2 +12x +10 All divided by 4(x+6)(x+1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[28x+282x^216x24+x^2+7x+6 \\ \text{ reorder terms } \\ (2x^2+x^2)+(28x16x+7x)+(2824+6) \\ (2+1)x^2+(2816+7)x+(2824+6) \\ 1x^2+19x+10 \\ x^2+19x+10\] is what I got for the numerator you might want to check my work

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0then how would i siplify it

freckles
 one year ago
Best ResponseYou've already chosen the best response.1in my mind \[\frac{x^2+19x+10}{4(x+1)(x+6)}\] this is simplified

freckles
 one year ago
Best ResponseYou've already chosen the best response.1however your teacher may want you to multiply the bottom out

freckles
 one year ago
Best ResponseYou've already chosen the best response.1not sure in your teacher's mind

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0can you help me with one more of these problems that similar..

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you can show me your work and I can help you fix it if it needs any fixing

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ 2} +\frac{ 15 }{ 2x14 }  \frac{ 3x5 }{ x^27x }\]

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0first one stays the same 2(x7) x(x7)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1check mark so far! :)

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0domain is all real numbers except when x=7

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you have x on the bottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{2}+\frac{15}{2(x7)}+\frac{3x5}{x(x7)} \\ \text{ so we want } x7 \neq 0 \text{ and also we want } x \neq 0\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1do you want to try to figure out what the denominators should be so we can combine the fractions? or do you want me to tell you and you try to figure out the new numerators?

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0you tell me and i try to figure out the numerators

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok notice the denominators are: 2 2(x7) x(x7)  if we look at just 2 and 2(x7) then the denominator would be 2(x7) but we also have x(x7) for the third bottom so looking at 2(x7) and x(x7) the new denominator of all them should be 2x(x7) this is because all the denominators given go into 2x(x7) that I can think of something to multiply all of your original denominators to get this new denominator of 2x(x7) for example: 2*x(x7) is 2x(x7) and 2(x7)*x is 2x(x7) and x(x7)*2 is 2x(x7)

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ 2 } * x(x7)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well you multiply top and bottom by x(x7)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{2} \cdot \frac{x(x7)}{x(x7)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{x(x7)}{2x(x7)}\] but yep this right for the first fraction

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0the next one you only need to multiply top and bottom by x

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0and the last one you only multiply it by 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1(well 2/2 but I get what you are saying) right!!! so we have: \[\frac{1}{2}+\frac{15}{2(x7)}+\frac{3x5}{x(x7)} \\ =\frac{x(x7)}{2x(x7)}+\frac{15x}{2x(x7)}+\frac{2(3x5)}{2x(x7)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so now we have the same denominators we can now combine the fractions

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{2}+\frac{15}{2(x7)}+\frac{3x5}{x(x7)} \\ =\frac{x(x7)}{2x(x7)}+\frac{15x}{2x(x7)}+\frac{2(3x5)}{2x(x7)} \\ =\frac{x(x7)+15x+2(3x5)}{2x(x7)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1multiply top out and combine like terms

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0so i can take the 2x out of the top and bottom and then i would get \[\frac{ x^210 }{ x7 }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1sorry my internet stopped working for a few minutes there

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and you can't cancel out common terms but you can cancel out common factors

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so you should have: \[\frac{1}{2}+\frac{15}{2(x7)}+\frac{3x5}{x(x7)} \\ =\frac{x(x7)}{2x(x7)}+\frac{15x}{2x(x7)}+\frac{2(3x5)}{2x(x7)} \\ =\frac{x(x7)+15x+2(3x5)}{2x(x7)} \\ =\frac{x^2+14x20}{2x(x7)}\]

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0so what would be the final equation

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{x^2+14x20}{2x(x7)}\] and you can multiply to the bottom out if you want or if your teacher wants but to me this is simplified

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0how did you get 14x and 20

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0the last fraction you are supppose to subtract

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the problem I have is: \[\frac{1}{2}+\frac{15}{2(x7)}+\frac{3x5}{x(x7)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1is that not the right problem?

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0sorry it was subtract the last fraction

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0thats how i got \[\frac{ x^2 +2x10 }{ 2x(x7) }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{2}+\frac{15}{2(x7)}\frac{3x5}{x(x7)} \\ =\frac{x(x7)}{2x(x7)}+\frac{15x}{2x(x7)}\frac{2(3x5)}{2x(x7)} \\ =\frac{x(x7)+15x2(3x5)}{2x(x7)} \\ =\frac{x^27x+15x6x+10}{2x(x7)}\] \[=\frac{x^2+2x+10}{2x(x7)}\]

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0why is it 2 for the rest it was +2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you have 2(3x5) distributive property says a(b+c)=ab+ac so this means 2(3x5) is 2(3x)+(2)(5) or 6x+10

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0why is it 2 cause it has +2 at bottom

18jonea
 one year ago
Best ResponseYou've already chosen the best response.0hence how i got x2+2x−10 / 2x(x−7)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{2}+\frac{15}{2(x7)}\color{red}\frac{3x5}{x(x7)} \\ =\frac{x(x7)}{2x(x7)}+\frac{15x}{2x(x7)}\color{red}\frac{2(3x5)}{2x(x7)} \\ =\frac{x(x7)+15x\color{red}2(3x5)}{2x(x7)} \\ =\frac{x^27x+15x6x+10}{2x(x7)} \\ =\frac{x^2+2x+10}{2x(x7)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1do you see that red subtraction symbol I just brought it down
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