Q13. - Algebra 1

Question

Simplify each expression.

$\frac{\frac{y^2+10y+24}{y^2-9}}{\frac{3y^2+17y-6}{2y^2-11y+15}}$

Step-by-Step Solution

Answer

$\frac{\left(y+4\right)\left(2y-5\right)}{\left(y+3\right)\left(3y-1\right)}$

Step 1. Division expression.

Write as a division expression.

$\frac{y^2+10y+24}{y^2-9}÷\frac{3y^2+17y-6}{2y^2-11y+15}$

Step 2. Divide.

To divide, multiply by the reciprocal.

 $\frac{y^2+10y+24}{y^2-9}\cdot \frac{2y^2-11y+15}{3y^2+17y-6}$

Step 3. Factor.

Factor the given expression and simplify.

 $\frac{\left(y+4\right)\left(y+6\right)}{\left(y+3\right)\left(y-3\right)}\cdot \frac{\left(2y-5\right)\left(y-3\right)}{\left(y+6\right)\left(3y-1\right)}=\frac{\left(y+4\right)\left(2y-5\right)}{\left(y+3\right)\left(3y-1\right)}$

Therefore, $\frac{\frac{y^2+10y+24}{y^2-9}}{\frac{3y^2+17y-6}{2y^2-11y+15}}$ can be simplified as $\frac{\left(y+4\right)\left(2y-5\right)}{\left(y+3\right)\left(3y-1\right)}$.