Question

What is the product x^2-16 over 2x+8 • x^3-2x^2+x over x^2+3x-4

Answer 1

Answer:

  $\dfrac{x^3-5x^2 +4x}{2x+8}$

Step-by-step explanation:

The basic idea is to factor each expression and cancel common factors from numerator and denominator.

  $\dfrac{x^2-16}{2x+8}\cdot\dfrac{x^3-2x^2 +x}{x^2+3x-4}=\dfrac{(x-4)(x+4)}{2(x+4)}\cdot\dfrac{x(x-1)^2}{(x+4)(x-1)}\\\\=\dfrac{(x-4)x(x-1)}{2(x+4)}\cdot\dfrac{(x+4)(x-1)}{(x+4)(x-1)}\\\\=\boxed{\dfrac{x^3-5x^2 +4x}{2x+8}}$