SOLUTION: Divide, and then simplify, if possible. 59.page#540 {{{((3n^2+5n-2)/(12n^2-13n+3))/((n^2+3n+2)/(4n^2+5n-6))}}} Simplify the rational expression 1). {{{(x^2+3x-10)/(x^2+x-2

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Divide, and then simplify, if possible. 59.page#540 {{{((3n^2+5n-2)/(12n^2-13n+3))/((n^2+3n+2)/(4n^2+5n-6))}}} Simplify the rational expression 1). {{{(x^2+3x-10)/(x^2+x-2      Log On

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Question 174122: Divide, and then simplify, if possible.
59.page#540
%28%283n%5E2%2B5n-2%29%2F%2812n%5E2-13n%2B3%29%29%2F%28%28n%5E2%2B3n%2B2%29%2F%284n%5E2%2B5n-6%29%29
Simplify the rational expression
1).
%28x%5E2%2B3x-10%29%2F%28x%5E2%2Bx-20%29
2). Divide:
%28%286x%5E2-x-12%29%2F%289x%5E2-16%29%29%2F%28%282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29%29
Answer by Edwin McCravy(6938) About Me  (Show Source):
You can put this solution on YOUR website!
%28%283n%5E2%2B5n-2%29%2F%2812n%5E2-13n%2B3%29%29%2F%28%28n%5E2%2B3n%2B2%29%2F%284n%5E2%2B5n-6%29%29 

Write that as the top fraction divided by the bottom fraction:

matrix%281%2C3%2C+%283n%5E2%2B5n-2%29%2F%2812n%5E2-13n%2B3%29%2C+%27%F7%27%2C+%28n%5E2%2B3n%2B2%29%2F%284n%5E2%2B5n-6%29%29 

Invert the second fraction and change division to multiplication:

matrix%281%2C3%2C+%283n%5E2%2B5n-2%29%2F%2812n%5E2-13n%2B3%29%2C+%27%D7%27%2C+%284n%5E2%2B5n-6%29%2F%28n%5E2%2B3n%2B2%29%29

Factor all numerators and denominators:

matrix%281%2C3%2C+%28%283n-1%29%28n%2B2%29%29%2F%28%284n-3%29%283n-1%29%29%2C+%27%D7%27%2C+%28%284n-3%29%28n%2B2%29%29%2F%28%28n%2B2%29%28n%2B1%29%29%29

Indicate the multiplication of both numerators and both denominators
as all just one fraction:

matrix%281%2C1%2C+%28%283n-1%29%28n%2B2%29%284n-3%29%28n%2B2%29%29%2F%28%284n-3%29%283n-1%29%28n%2B2%29%28n%2B1%29%29%29

Cancel the %283n-1%29's, the %28n%2B2%29's and the %28%24n-3%29's

matrix%281%2C1%2C+%28%28cross%283n-1%29%29%28cross%28n%2B2%29%29%28cross%284n-3%29%29%28n%2B2%29%29%2F%28%28cross%284n-3%29%29%28cross%283n-1%29%29%28cross%28n%2B2%29%29%28n%2B1%29%29%29

All that's left is

%28n%2B2%29%2F%28n%2B1%29

------------

%28x%5E2%2B3x-10%29%2F%28x%5E2%2Bx-20%29

Factor the numerator and denominator:

%28%28x-2%29%28x%2B5%29%29%2F%28%28x%2B5%29%28x-4%29%29 

Cancel the %28x%2B5%29's

%28%28x-2%29%28cross%28x%2B5%29%29%29%2F%28%28cross%28x%2B5%29%29%28x-4%29%29

All that's left is

%28x-2%29%2F%28x-4%29

----------------

The last one is done exactly the same way as the first one.
The answer is

%28x%2B1%29%2F%28x-2%29

See if you can follow the same steps and get that answer.

Edwin