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 ->  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


   

Question 174122: Divide, and then simplify, if possible.
59.page#540

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(20055) About Me  (Show Source):
You can put this solution on YOUR website!


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

 

Invert the second fraction and change division to multiplication:



Factor all numerators and denominators:



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



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



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