Question 183233


{{{(6x^2-11x-10)/(2x^2-9x+10)}}} Start with the given expression.



{{{((3x+2)(2x-5))/(2x^2-9x+10)}}} Factor {{{6x^2-11x-10}}} to get {{{(3x+2)(2x-5)}}}.



{{{((3x+2)(2x-5))/((x-2)(2x-5))}}} Factor {{{2x^2-9x+10}}} to get {{{(x-2)(2x-5)}}}.



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



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



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



So {{{(6x^2-11x-10)/(2x^2-9x+10)}}} simplifies to {{{(3x+2)/(x-2)}}}.



In other words, {{{(6x^2-11x-10)/(2x^2-9x+10)=(3x+2)/(x-2)}}} where {{{x<>-5/2}}} or {{{x<>2}}}