Q12. - Algebra 1

Question

Simplify each expression.

$\frac{\frac{a-4}{a^2+6a+8}}{\frac{a^2-3a-4}{a^2-a-6}}$

Step-by-Step Solution

Answer

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

Step 1. Division expression.

Write as a division expression.

 $\frac{a-4}{a^2+6a+8}÷\frac{a^2-3a-4}{a^2-a-6}$

Step 2. Divide.

To divide, multiply by the reciprocal.

$\frac{a-4}{a^2+6a+8}\cdot \frac{a^2-a-6}{a^2-3a-4}$

Step 3. Factor.

Factor the given expression and simplify.

 $\frac{\left(a-4\right)}{\left(a+2\right)\left(a+4\right)}\cdot \frac{\left(a+2\right)\left(a-3\right)}{\left(a-4\right)\left(a+1\right)}=\frac{\left(a-3\right)}{\left(a+4\right)\left(a+1\right)}$ 

 Therefore, $\frac{\frac{a-4}{a^2+6a+8}}{\frac{a^2-3a-4}{a^2-a-6}}$ can be simplified as $\frac{\left(a-3\right)}{\left(a+4\right)\left(a+1\right)}$.