Question

Which expression is equal to 2x^2+2x−40/4x^2−12x−16 ⋅ 3x^2−3/x^2−5x

3(x+1)/2x

3(x−1)/2x

3(x−1)(x+5)/2x(x−5)

3(x−1)(x+4)/2x(x−4)

Answer 1

3(x−1)(x+5)/(2x(x−5))

Explanation:

In general simplifying something like this requires you factor the various polynomials to see what factors may cancel.

`(2x^2+2x-40)/(4x^2-12x-16)\cdot(3x^2-3)/(x^2-5x)=(2(x-4)(x+5)\cdot 3(x-1)(x+1))/(4(x-4)(x+1)\cdot x(x-5))\\\\=(3(x-1)(x+5))/(2x(x-5))`