anonymous
  • anonymous
subtract: y/y-2 - 8+y/2-y
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
This is tricky... you need to know this fact. 2 - y = -(y - 2) you can always flip numbers around a - sign and multiply by a - so 5 - x = -(x - 5)
anonymous
  • anonymous
In this case you want the 2 - y to be y - 2 because you need a common denominator. so you turn the bottom in to y - 2 and then you put a - sign out in front... In this case that negative sign out front would turn your problem into a + sign y/y-2 + 8 + y/y - 2 Now you have common denominators y + 8 + y -------- y - 2 2y + 8 ------ y - 2
anonymous
  • anonymous
omg hi again!!!

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anonymous
  • anonymous
this was our next question
anonymous
  • anonymous
OK... I just found you... do you get this?
anonymous
  • anonymous
i dont understand how you get the common denom....
anonymous
  • anonymous
Well... y - 2 and 2 - y are opposites of each other.... you should be able to see that if you flip the one on the right around the minus sign it becomes the y - 2 ex. 2 - y flips to y - 2 OK?
anonymous
  • anonymous
then you have to change the subtraction to addition??
anonymous
  • anonymous
Yes... because it is the opposite you have to put a - sign out in front, and actually you change the sign of the problem... so in this case the subtraction becomes addition. This is a hard concept.
anonymous
  • anonymous
hmmm then what
anonymous
  • anonymous
Then you have a common denominator... so if you look above to my steps you will see that you put everything on the top over y - 2 because you now have a common denominator
anonymous
  • anonymous
7/T-2 - 6/T^2-2T - 3/T is the LCD T^2-2T?
anonymous
  • anonymous
7 6 3 ---- - ----------- - ------ T - 2 T^2 - 2T T T - 2 factors into (T - 2) T^2 - 2T factors into T(T - 2) T factors into T Common denominator is T(T - 2) or T^2 - 2T easier if you write it T(T - 2)
anonymous
  • anonymous
T(T - 2) * 7 T(T - 2) * 6 T(T - 2) * 3 ------------ - ---------- - ---------- (T - 2) T(T - 2) T
anonymous
  • anonymous
The (T - 2)'s cancel in the first fraction The T and (T - 2) cancel in the second fraction The T cancels in the third fraction
anonymous
  • anonymous
7t-6-3t-2 ??
anonymous
  • anonymous
7T - 6 - 3(t - 2) 7T - 6 - 3T + 6 4T
anonymous
  • anonymous
isnt it -6?
anonymous
  • anonymous
left with 4t-12
anonymous
  • anonymous
The - sign goes with the 3 so it is actually -3(T - 2) and -3 * -2 = +6
anonymous
  • anonymous
ohhh got it
anonymous
  • anonymous
meeee tooooooo!
anonymous
  • anonymous
YEAH!!!!!
anonymous
  • anonymous
5-x/x-1 / 2-x/x+1
anonymous
  • anonymous
5 - x 2 - x ---- divided by ----- x - 1 x + 1 write the divide sign that has a --- with a dot above and below. Are you sure this is what you want.
anonymous
  • anonymous
noooo wait hold on
anonymous
  • anonymous
X 5- ---- X-1 ___________ X 2- ---- X+1
anonymous
  • anonymous
yes!
anonymous
  • anonymous
OK... First we will simplify the top. 5 x - - ---- 1 x- 1 what is the common denominator?
anonymous
  • anonymous
x-1?
anonymous
  • anonymous
(x - 1)*5 x ------- - ----- x - 1 x - 1
anonymous
  • anonymous
5x - 5 x ----- - ----- x - 1 x - 1 4x - 5 ------ x - 1 ok?
anonymous
  • anonymous
5X+1-X --------- X-1
anonymous
  • anonymous
GOT IT
anonymous
  • anonymous
Yes... now add the x's
anonymous
  • anonymous
Now let's do the same to the bottom.
anonymous
  • anonymous
X+2 ----- X+1
anonymous
  • anonymous
2 x - - ---- 1 x + 1 (x + 1)*2 x -------- - ---- (x + 1)*1 x + 1 (x + 1) *2 x -------- - ----- x + 1 x + 1 2x + 2 - x --------- x + 1 x + 2 ---- x + 1
anonymous
  • anonymous
OOPS... go back to the first one... you have 4x - 1 look at mine... it is 4x - 5.. you have to distribute.
anonymous
  • anonymous
got it
anonymous
  • anonymous
4x - 5 x + 2 ------ divided by ------ x - 1 x + 1 Now.... when ever you have a fraction divided by a fraction. you ALWAYS multiply by the reciprocal
anonymous
  • anonymous
4X+5 ------ X+1 -------- X+2 --- X+1
anonymous
  • anonymous
4x - 5 x + 1 ------ x ----- x - 1 x + 2
anonymous
  • anonymous
top right and bottom left cancel out?
anonymous
  • anonymous
4X+5 ------ X+2
anonymous
  • anonymous
amazing... go back and look at the numerator.. it is 4x - 5
anonymous
  • anonymous
4X-5 ------ X+2 ????? I HOPE
anonymous
  • anonymous
I wish they did cancel... they usually do.. but not here a (x - 1) can ONLY cancel with an (x - 1) and a (x + 1) can ONLY cancel with (x + 1) Usually you CAN cancel, but not in this problem. You would multiply the numerators (FOIL METHOD) then multiply the denominators (FOIL METHOD) and you would have your answer
anonymous
  • anonymous
so now what!?!?!!? omg im lost now
anonymous
  • anonymous
(4x - 5)(x + 1) ------------- (x - 1)(x + 2) 4x^2 + 4x - 5x - 5 ---------------- x^2 + 2x - x - 2 4x^2 - x - 5 ----------- x^2 + x - 2
anonymous
  • anonymous
Unless you did not type in the original problem correctly? otherwise this is the answer.
anonymous
  • anonymous
i got that
anonymous
  • anonymous
Good.
anonymous
  • anonymous
i wanna cry this is hard
anonymous
  • anonymous
solve for X: (4x-7)^2 = -27 :)
anonymous
  • anonymous
They are just a lot of steps.
anonymous
  • anonymous
(4x - 7)^2 = -27 Are you sure this is correct?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
yessssssssss
anonymous
  • anonymous
OK.. so you know what imaginary numbers are i's
anonymous
  • anonymous
yes !
anonymous
  • anonymous
OK.. what if I gave you this problem... do you know what to do. x^2 = 16
anonymous
  • anonymous
yes square root both sides
anonymous
  • anonymous
Good... so in this problem you have (something)^2 = -27 so you square root both sides
anonymous
  • anonymous
x=4
anonymous
  • anonymous
(4x - 7)^2 = -27 4x - 7 = sqrt(-27)
anonymous
  • anonymous
sqrt(-27) is -3i sqrt(3) do you understand this?
anonymous
  • anonymous
\[3i \sqrt{3?}\]
anonymous
  • anonymous
yess!
anonymous
  • anonymous
OOPS you are correct is is positive
anonymous
  • anonymous
4x - 7 = 3i sqrt(3) 4x = 3i sqrt(3) + 7 x = 3i sqrt(3) + 7 ------------ 4
anonymous
  • anonymous
\[9+3x-2x ^{2} \over x ^{2}-16 \]
anonymous
  • anonymous
wait im not done hold on!
anonymous
  • anonymous
all that divided by \[4x ^{3}-9x \over 2x ^{2}+5x-12\]
anonymous
  • anonymous
simplify and state restricitons
anonymous
  • anonymous
-2x^2 + 3x + 9 2x^2 + 5x - 12 --------------- x ------------- x^2 - 16 4x^3 - 9x since it is a fraction divide by a fraction.. we are going to turn it into a multiply problem right away by using the reciprocal. OK?
anonymous
  • anonymous
ok hold on lemme take all that in
anonymous
  • anonymous
then factor?
anonymous
  • anonymous
yes we have to factor all four... but it is difficult to factor when there is a negative in front of the x^2 so for the first fraction in the numerator we are going to factor out a - sign first. - (2x^2 - 3x - 9)
anonymous
  • anonymous
-(2x + 3)(x - 3) (2x - 3)(x + 4) -------------- x ------------- (x + 4)(x - 4) x(4x^2 - 9) x(2x + 3)(2x - 3)
anonymous
  • anonymous
-(2x+3)(x-3) (x+4) (2x-3) ---------- ------------ (x+4) (x-4) x(2x+3) (2x-3)
anonymous
  • anonymous
now we can cancel out right?
anonymous
  • anonymous
Yes... now cancel anything in ( )'s with like ( )'s Anything on the top with anything on the bottom that matches.
anonymous
  • anonymous
x-3 ----- x(x-4)
anonymous
  • anonymous
close you still have that - sign on top -(x - 3) ------- x(x - 4) they may want it like -x + 3 ------ x^2 - 4x it is all the same...
anonymous
  • anonymous
Now you also said you had to tell restrictions.
anonymous
  • anonymous
yesss
anonymous
  • anonymous
OK... go back to the factored fractions. The rule is you can NEVER divide by 0 so whatever makes those ( )'s 0 would be a restriction.
anonymous
  • anonymous
We are only concerned with the denominators.
anonymous
  • anonymous
okkk
anonymous
  • anonymous
(x + 4)(x - 4) x(2x + 3)(2x - 3)
anonymous
  • anonymous
-4,4 -3/2, 3/2
anonymous
  • anonymous
And one more you need 0 because of the single x Every where there is an x there is a restriction.
anonymous
  • anonymous
blexting you are great!!! we have 3 more can we keep going?
anonymous
  • anonymous
Sure
anonymous
  • anonymous
way better then our professor!
anonymous
  • anonymous
X^2-9 ---------------- X^3+X^2-9X-9 SIMPLIFY
anonymous
  • anonymous
Factor
anonymous
  • anonymous
(x + 3)(x - 3) ------------
anonymous
  • anonymous
When you have 4 terms you should try this first. Take the first two terms and take out a common factor. x^3 + x^2 = x^2(x + 1) Take the last two terms and do the same thing. -9x - 9 = -9(x + 1) OK?
anonymous
  • anonymous
x+1 is the answer right?
anonymous
  • anonymous
(X^2-9) (X+1)
anonymous
  • anonymous
I MEAN (X-1)
anonymous
  • anonymous
OK.. Now you have x^2(x + 1) - 9(x + 1) ... good amozing. because (x + 1) is a common factor you now have (x + 1)(x^2 - 9) BUT this is the difference of two squares. (x + 1)(x + 3)(x - 3)
anonymous
  • anonymous
they dont cancel out
anonymous
  • anonymous
?
anonymous
  • anonymous
So you have the top which is (x + 3)(x - 3) ------------ (x + 1)(x + 3)(x - 3) then cancel and you are left with 1 ------- x + 1 with restrictions of x cannot be -1,-3 or 3
anonymous
  • anonymous
solve for X: 3 17 7 ------- = ---- - ----- 4x+2 2 2x+1
anonymous
  • anonymous
Common denominator 4x + 2 = 2(2x + 1) 2 = 2 2x + 1 = 2x + 1 common denominator 2(2x + 1)
anonymous
  • anonymous
Put that on top of each fraction and then cancel with the denominators.
anonymous
  • anonymous
2(2x + 1) * 3 2(2x + 1) * 17 2(2x + 1) * 7 ----------- = ------------- - ----------- 2(2x + 1) 2 2x + 1
anonymous
  • anonymous
34X+3=3 ??
anonymous
  • anonymous
X=1/34
anonymous
  • anonymous
3 = 17(2x + 1) - 14 3 = 34x + 17 - 14 3 = 34x + 3 0 = 34x 0 = x
anonymous
  • anonymous
amozing when you take 34x + 3 = 3 and you subtract 3 you get 34x = 0
anonymous
  • anonymous
Restrictions x cannot be -1/2
anonymous
  • anonymous
GOT IT, THANKS!! ONE MORE :)
anonymous
  • anonymous
OK
anonymous
  • anonymous
X^2+XY-2Y^2 X ----------- X ----------------- X^3+X^2Y X^2+3XY+2Y^2
anonymous
  • anonymous
3X^3Y^2
anonymous
  • anonymous
NOT 3Y JUST Y SORRY
anonymous
  • anonymous
(x + 2y)(x - y) x ------------ times -------------- x^2(x + y) (x + 2y)(x + y)
anonymous
  • anonymous
(x - y) ------------ x(x + y)^2
anonymous
  • anonymous
GOT IT THANKS!!
anonymous
  • anonymous
gixxergirl..... did you leave us?
anonymous
  • anonymous
Are we done????
anonymous
  • anonymous
lol sorry i had to pee!!! but thank you so mucchhhhh for everythinggg !!! are you a math teacher?
anonymous
  • anonymous
yes I am in a high school
anonymous
  • anonymous
YOU HAVE BEEN SO HELPFUL!! THANK YOU SO MUCH
anonymous
  • anonymous
No problem.. if you see me on here again and want help.. just holler. Have a wonderful Easter... He is risen!!! Good night.

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