Question

In the following exercises, multiply.

$\frac{z^2+3z}{z^2-3z-4}·\frac{z-4}{z^2}$

Short answer

The required answer is$\frac{z+3}{z\left(z+1\right)}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{z^2+3z}{z^2-3z-4}·\frac{z-4}{z^2}$

Step 2. Simplify the expression.

$\frac{z^2+3z}{z^2-3z-4}·\frac{z-4}{z^2}$

Factor the numerator and denominator completely,

$\frac{z\left(z+3\right)}{\left(z-4\right)\left(z+1\right)}·\frac{z-4}{z^2}$

Multiply the numerators and denominators,

$\frac{z\left(z+3\right)\left(z-4\right)}{z·z\left(z-4\right)\left(z+1\right)}$

Simplify by dividing out common factors,

$\frac{z+3}{z\left(z+1\right)}$