Question 174833
{{{((20+7x-3x^2)/(x^2-16))/((6x+10)/(2x^2+5x-12))}}} Start with the given expression.



{{{((-3x^2+7x+20)/(x^2-16))/((6x+10)/(2x^2+5x-12))}}} Rearrange the terms.



{{{((-3x^2+7x+20)/(x^2-16))((2x^2+5x-12)/(6x+10))}}} Multiply the first fraction {{{(-3x^2+7x+20)/(x^2-16)}}} by the reciprocal of the second fraction {{{(6x+10)/(2x^2+5x-12)}}}.



{{{((-(3x+5)(x-4))/(x^2-16))((2x^2+5x-12)/(6x+10))}}} Factor {{{-3x^2+7x+20}}} to get {{{-(3x+5)(x-4)}}}.



{{{((-(3x+5)(x-4))/((x-4)(x+4)))((2x^2+5x-12)/(6x+10))}}} Factor {{{x^2-16}}} to get {{{(x-4)(x+4)}}}.



{{{((-(3x+5)(x-4))/((x-4)(x+4)))(((x+4)(2x-3))/(6x+10))}}} Factor {{{2x^2+5x-12}}} to get {{{(x+4)(2x-3)}}}.



{{{((-(3x+5)(x-4))/((x-4)(x+4)))(((x+4)(2x-3))/(2(3x+5)))}}} Factor {{{6x+10}}} to get {{{2(3x+5)}}}.



{{{(-(3x+5)(x-4)(x+4)(2x-3))/(2(x-4)(x+4)(3x+5))}}} Combine the fractions. 



{{{-(highlight((3x+5))highlight((x-4))highlight((x+4))(2x-3))/(2*highlight((x-4))highlight((x+4))highlight((3x+5)))}}} Highlight the common terms. 



{{{-(cross((3x+5))cross((x-4))cross((x+4))(2x-3))/(2*cross((x-4))cross((x+4))cross((3x+5)))}}} Cancel out the common terms. 



{{{-(2x-3)/(2)}}} Simplify. 




So {{{((20+7x-3x^2)/(x^2-16))/((6x+10)/(2x^2+5x-12))}}} simplifies to {{{-(2x-3)/(2)}}}.