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anonymous
 one year ago
x^2  2x  5/x  3 ÷ x  5/x^2  9
anonymous
 one year ago
x^2  2x  5/x  3 ÷ x  5/x^2  9

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Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0factor the quadratic equation

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge\rm \frac{ \frac{ x^22x5 }{ x3 } }{ \frac{ x5 }{ x^29 }}\] and change division to multiplication to do that multiply top fraction with the RECIPROCAL of the bottom fraction example \[\huge\rm \frac{ \frac{ a }{ b } }{ \frac{ c }{ d } }=\frac{ a }{ b } \times \frac{ d }{ c}\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{ x^22x5 }{ x3 } \div \frac{ x5 }{ x^29 }\] you need to factor the numerator \[(x^22x5)\] and remember when you divide by fractions you flip the second fraction and multiply, \[\frac{ a }{ b } \div \frac{ c }{ d } \implies \frac{ a }{ b } \times \frac{ d }{ c }\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0x^29 apply difference of squares rule \[\huge\rm a^2b^2 =(a+b)(ab)\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2You will have to complete the square or use quadratic formula for x^22x5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm trying to keep up! Could you run me through the factoring process really quickly? I think I must be doing something wrong because my results don't match any of the possible answers.

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0are you sure its x^22x5 ??

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Yeah I don't think that's right either haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm so sorry! It's x^2  2x  15, not 5. But the rest should be right!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Oh ok so now just find two numbers that add up to 2 and multiply together to give 15, can you think of two?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0\(\color{blue}{\text{Originally Posted by}}\) @Juliette2120 I'm trying to keep up! Could you run me through the factoring process really quickly? I think I must be doing something wrong because my results don't match any of the possible answers. \(\color{blue}{\text{End of Quote}}\) show your work plz :)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3did you factor x^29 yet @Juliette2120

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2So you have \[\frac{ (x5)(x+3) }{ x3 } \times \frac{ x^29 }{ x5 }\] now you can notice we can cancel out some terms, but lets first factor \[x^29\] as nnesha mentioned here \(\color{blue}{\text{Originally Posted by}}\) @Nnesha x^29 apply difference of squares rule \[\huge\rm a^2b^2 =(a+b)(ab)\] \(\color{blue}{\text{End of Quote}}\)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3an example \[x^225=(x5)(x+5) \\ \text{ notice: I just replaced } a \text{ with } x \text{ and } b \text{ with 5 } \\ \text{ since } x^225=x^25^2\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3can you write 9 as a some number squared?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3right so a is x and b is 3 in this case

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3\[x^29=x^23^2 \\ x^23^2=(x3)(x+3)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Astrophysics I'm having a difficult time understanding the difference of squares rule! Could you explain that to me? Or show me how to factor this specific example?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@myininaya Okay! I understand this. What's the next step?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Well @myininaya just showed it but, it can be a bit tricky as it's not very intuitive to go from \[a^2b^2 \implies (a+b)(ab)\] unless you distribute \[(a+b)(ab)\] itself

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ x^22x15 }{ x3 } \div \frac{ x5 }{ x^29 } \\ \frac{x^22x15}{x3} \times \frac{x^29}{x5} \]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2I guess for now just remember it, \[a^2b^2 \implies x^23^2 \]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3notice to change it to multiplication we just flip the second fraction

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3now let's put in all of our factored forms

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{(x5)(x+3)}{x3} \cdot \frac{(x3)(x+3)}{x5} \\ \frac{(x5)(x+3)(x3)(x+3)}{(x3)(x5)}\] do you see anything that cancels?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do they have to be on the same level to cancel?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0\(\color{blue}{\text{Originally Posted by}}\) @Juliette2120 @Astrophysics I'm having a difficult time understanding the difference of squares rule! Could you explain that to me? Or show me how to factor this specific example? \(\color{blue}{\text{End of Quote}}\) take square root of both terms (sqrt of 1st term + sqrt of 2nd term)(sqrt of 1st term  sqrt of 2nd term) easy to remember.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3you have to have a factor on top that matches a factor on bottom to cancel that common factor

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it would be (x  5) and (x  3)?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Nope you can always factor them out, also remember for example\[\frac{ (x+1) }{ (x+1) } = 1\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2I guess I'll let @myininaya help you too much information all at once lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Astrophysics I'm sorry about that! You've both been very helpful  it's all making a bit more sense!

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3as you see you have an (x5) on top and bottom so as @Astrophysics says (x5)/(x5)=1

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3or in other words you can cancel the (x5) on top with the one on bottom

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3do you see anything else that can cancel?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3yes \[\frac{(x5)(x+3)}{x3} \cdot \frac{(x3)(x+3)}{x5} \\ \frac{\cancel{(x5)}(x+3)\cancel{(x3)}(x+3)}{\cancel{(x3)}\cancel{(x5)}} \]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{(x+3)(x+3)}{1} \text{ or } (x+3)(x+3)\] do you know how to multiply (x+3)(x+3) out?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So... It would be (x + 3)^2?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3can we leave it as (x+3)^2?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3or do they want it in standard form?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes! That's an answer!

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3k! do you want to talk more about the difference of squares formula?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Trust me  I will be back shortly with more questions! I've been doing really well with math, but for some reason this module has me stumped!

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3just in case you need something to look back on in the future: \[(ab)(a+b) =a(a+b)b(a+b) \\ (ab)(a+b)=a(a)+a(b)b(a)b(b) \\ (ab)(a+b)=a^2+ababb^2 \\ (ab)(a+b)=a^2b^2 \\ \text{ Examples: } \\ x^21=(x1)(x+1) \\ x^24=(x2)(x+2) \\ x^29=(x3)(x+3) \\ x^216=(x4)(x+4) \\ x^225=(x5)(x+5) \\ \text{ More Examples: } \\ 4x^225=(2x5)(2x+5) \text{ note: I hope you see that } 4x^2=(2x)^2 \text{ and } 25=5^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much! I'll keep that!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks to all of you for your help! @myininaya @Astrophysics @Nnesha

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3@Astrophysics and @Nnesha are the most awesomest! :) Yes I know that isn't a word. And @Juliette2120 you did great too.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Haha, thanks and no problem! Everyone was great! XD
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