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

1 Answer

Answer:

#\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)}#