Question

Simplify each expression.

$\frac{\mathbf{x}\mathbf{+}\mathbf{4}}{{\mathbf{x}}^2\mathbf{+}\mathbf{12}\mathbf{x}\mathbf{+}\mathbf{32}}$

Short answer

The given expression can be simplified to $\frac{1}{\mathbf{x}\mathbf{+}\mathbf{8}}$.

Step-by-step solution

Step 1. Simplify rational function.

Let $x,y$, and $z$, be polynomials with$x\ne 0$ and $z\ne 0$.

$\frac{yx}{zx}=\frac{y\cdot x}{z\cdot x}=\frac{y}{z}$

Step 2. Factor.

Factor denominator.

$\frac{x+4}{(x+4)(x+8)}$

Step 3. Divide.

Divide out common factors.
$\frac{1}{x+8}$

Therefore, the given expression can be simplified to $\frac{1}{x+8}$.