Question

How do you simplify `((x^2-2x-4)/(x^2+2x-8))*((3x^2+15x)/(x+1))/((4x^2-100)/(x^2-x-20))`?

Answer 1

`\frac{3x(x^2-2x-4)}{4(x+1)(x-2)}`

Explanation:

Given that

`(\frac{x^2-2x-4}{x^2+2x-8})\cdot \frac{\frac{3x^2+15x}{x+1}}{\frac{4x^2-100}{x^2-x-20}}`

`=(\frac{x^2-2x-4}{(x+4)(x-2)})\cdot \frac{\frac{3x(x+5)}{x+1}}{\frac{4(x+5)(x-5)}{(x-5)(x+4)}}`

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

`=\frac{(x^2-2x-4)}{(x-2)}\cdot \frac{3x}{4(x+1)}`

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