Q6. - Algebra 2

Question

Simplify the expression $\frac{6y^3-9y^2}{2y^2+5y-12}$.

Step-by-Step Solution

Answer

The simplified value of expression is $\frac{3y^2}{y+4}$.

Step 1. Write down the given expression.

The given expression is $\frac{6y^3-9y^2}{2y^2+5y-12}$.

Step 2. Simplify the expression.

The given expression $\frac{6y^3-9y^2}{2y^2+5y-12}$ is simplified as:

$\begin{array}{l}\frac{6y^3-9y^2}{2y^2+5y-12}=\frac{3y^2\left(2y-3\right)}{2y^2-3y+8y-12}\\ =\frac{3y^2\left(2y-3\right)}{y\left(2y-3\right)+4\left(2y-3\right)}\\ =\frac{3y^2\left(2y-3\right)}{\left(2y-3\right)\left(y+4\right)}\\ =\frac{3y^2}{y+4}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{3y^2}{y+4}$.