Question 174122
{{{((3n^2+5n-2)/(12n^2-13n+3))/((n^2+3n+2)/(4n^2+5n-6))}}} 
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Write that as the top fraction divided by the bottom fraction:

{{{matrix(1,3, (3n^2+5n-2)/(12n^2-13n+3), "÷", (n^2+3n+2)/(4n^2+5n-6))}}} 

Invert the second fraction and change division to multiplication:

{{{matrix(1,3, (3n^2+5n-2)/(12n^2-13n+3), "×", (4n^2+5n-6)/(n^2+3n+2))}}}

Factor all numerators and denominators:

{{{matrix(1,3, ((3n-1)(n+2))/((4n-3)(3n-1)), "×", ((4n-3)(n+2))/((n+2)(n+1)))}}}

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

{{{matrix(1,1, ((3n-1)(n+2)(4n-3)(n+2))/((4n-3)(3n-1)(n+2)(n+1)))}}}

Cancel the {{{(3n-1)}}}'s, the {{{(n+2)}}}'s and the {{{($n-3)}}}'s

{{{matrix(1,1, ((cross(3n-1))(cross(n+2))(cross(4n-3))(n+2))/((cross(4n-3))(cross(3n-1))(cross(n+2))(n+1)))}}}

All that's left is

{{{(n+2)/(n+1)}}}

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{{{(x^2+3x-10)/(x^2+x-20)}}}

Factor the numerator and denominator:

{{{((x-2)(x+5))/((x+5)(x-4))}}} 

Cancel the {{{(x+5)}}}'s

{{{((x-2)(cross(x+5)))/((cross(x+5))(x-4))}}}

All that's left is

{{{(x-2)/(x-4)}}}

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

{{{(x+1)/(x-2)}}}

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

Edwin</pre>