Question

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Answer 1

Simplifying $\frac{\frac{4x^2+2x}{x^2+x-2}}{\frac{8x^2+4x}{3x^2+10x+8}}$ we get $=\frac{3x+4}{2(x-1)}$

Option D is correct.

Step-by-step explanation:

We need to simplify:

$\frac{\frac{4x^2+2x}{x^2+x-2}}{\frac{8x^2+4x}{3x^2+10x+8}}$

It can be written as:

$\frac{4x^2+2x}{x^2+x-2}\div {\frac{8x^2+4x}{3x^2+10x+8}\\=\frac{2x(2x+1)}{x^2+2x-x-2}\div {\frac{4x(2x+1}{3x^2+6x+4x+8}\\=\frac{2x(2x+1)}{x(x+2)-1(x+2)}\div {\frac{4x(2x+1}{3x(x+2)+4(x+2)}$

$=\frac{2x(2x+1)}{(x-1)(x+2)}\div {\frac{4x(2x+1)}{(3x+4)(x+2)}$

Converting division sign into multiplication:

$=\frac{2x(2x+1)}{(x-1)(x+2)}\times \frac{(3x+4)(x+2)}{4x(2x+1)}$

Simplifying:

$=\frac{3x+4}{2(x-1)}$

So, simplifying $\frac{\frac{4x^2+2x}{x^2+x-2}}{\frac{8x^2+4x}{3x^2+10x+8}}$ we get $=\frac{3x+4}{2(x-1)}$

Option D is correct.

Keywords: Simplify the Rational Expression

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