Question

Can someone please help? Thank you!

Answer 1

Answer:

$\dfrac{2x(5x+1)}{4x-1}$

Step-by-step explanation:

Given expression:

$\dfrac{\dfrac{4x^3-12x^2}{4x^2+7x-2}}{\dfrac{2x^2-6x}{5x^2+11x+2}}$

Consider the numerator and the denominator separately.

Numerator:

$\dfrac{4x^3-12x^2}{4x^2+7x-2}\\ \\=\dfrac{4x^2(x-3)}{4x^2+8x-x-2}\\ \\=\dfrac{4x^2(x-3)}{4x(x+2)-(x+2)}\\ \\=\dfrac{4x^2(x-3)}{(x+2)(4x-1)}$

Denominator:

$\dfrac{2x^2-6x}{5x^2+11x+2}\\ \\=\dfrac{2x(x-3)}{5x^2+10x+x+2}\\ \\=\dfrac{2x(x-3)}{5x(x+2)+(x+2)}\\ \\=\dfrac{2x(x-3)}{(x+2)(5x+1)}$

The whole expression:

$\dfrac{\dfrac{4x^3-12x^2}{4x^2+7x-2}}{\dfrac{2x^2-6x}{5x^2+11x+2}}\\ \\ \\=\dfrac{\dfrac{4x^2(x-3)}{(x+2)(4x-1)}}{\dfrac{2x(x-3)}{(x+2)(5x+1)}}\\ \\ \\=\dfrac{4x^2(x-3)}{(x+2)(4x-1)}\cdot \dfrac{(x+2)(5x+1)}{2x(x-3)}\\ \\ \\=\dfrac{2x(5x+1)}{4x-1}$