Question

Can someone please help? Thank you!

Answer 1

`(2x(5x+1))/(4x-1)`

Explanation:

Given expression:

`((4x^3-12x^2)/(4x^2+7x-2))/((2x^2-6x)/(5x^2+11x+2))`

Consider the numerator and the denominator separately.

Numerator:

`(4x^3-12x^2)/(4x^2+7x-2)\\ \\=(4x^2(x-3))/(4x^2+8x-x-2)\\ \\=(4x^2(x-3))/(4x(x+2)-(x+2))\\ \\=(4x^2(x-3))/((x+2)(4x-1))`

Denominator:

`(2x^2-6x)/(5x^2+11x+2)\\ \\=(2x(x-3))/(5x^2+10x+x+2)\\ \\=(2x(x-3))/(5x(x+2)+(x+2))\\ \\=(2x(x-3))/((x+2)(5x+1))`

The whole expression:

`((4x^3-12x^2)/(4x^2+7x-2))/((2x^2-6x)/(5x^2+11x+2))\\ \\ \\=((4x^2(x-3))/((x+2)(4x-1)))/((2x(x-3))/((x+2)(5x+1)))\\ \\ \\=(4x^2(x-3))/((x+2)(4x-1))\cdot ((x+2)(5x+1))/(2x(x-3))\\ \\ \\=(2x(5x+1))/(4x-1)`