Question 325270


{{{((x^2-4)/(x^2-7x+10))/((x^2+6x+5)/(x^2-25))}}} Start with the given expression.



{{{((x^2-4)/(x^2-7x+10))((x^2-25)/(x^2+6x+5))}}} Multiply the first fraction {{{(x^2-4)/(x^2-7x+10)}}} by the reciprocal of the second fraction {{{(x^2+6x+5)/(x^2-25)}}}.



{{{(((x-2)(x+2))/(x^2-7x+10))((x^2-25)/(x^2+6x+5))}}} Factor {{{x^2-4}}} to get {{{(x-2)(x+2)}}}.



{{{(((x-2)(x+2))/((x-2)(x-5)))((x^2-25)/(x^2+6x+5))}}} Factor {{{x^2-7x+10}}} to get {{{(x-2)(x-5)}}}.



{{{(((x-2)(x+2))/((x-2)(x-5)))(((x-5)(x+5))/(x^2+6x+5))}}} Factor {{{x^2-25}}} to get {{{(x-5)(x+5)}}}.



{{{(((x-2)(x+2))/((x-2)(x-5)))(((x-5)(x+5))/((x+5)(x+1)))}}} Factor {{{x^2+6x+5}}} to get {{{(x+5)(x+1)}}}.



{{{((x-2)(x+2)(x-5)(x+5))/((x-2)(x-5)(x+5)(x+1))}}} Combine the fractions. 



{{{(highlight((x-2))(x+2)highlight((x-5))highlight((x+5)))/(highlight((x-2))highlight((x-5))highlight((x+5))(x+1))}}} Highlight the common terms. 



{{{(cross((x-2))(x+2)cross((x-5))cross((x+5)))/(cross((x-2))cross((x-5))cross((x+5))(x+1))}}} Cancel out the common terms. 



{{{(x+2)/(x+1)}}} Simplify. 



So {{{((x^2-4)/(x^2-7x+10))/((x^2+6x+5)/(x^2-25))}}} simplifies to {{{(x+2)/(x+1)}}}.



In other words, {{{((x^2-4)/(x^2-7x+10))/((x^2+6x+5)/(x^2-25))=(x+2)/(x+1)}}}