Question

Simplify the expression $\frac{y^2+4y+4}{3y^2+5y-2}$.

Short answer

The simplified value of expression is $\frac{y+2}{3y-1}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $\frac{y^2+4y+4}{3y^2+5y-2}$.

Step 2. Simplify the expression.

The given expression $\frac{y^2+4y+4}{3y^2+5y-2}$is simplified as:

$\begin{array}{l}\frac{y^2+4y+4}{3y^2+5y-2}=\frac{{\left(y+2\right)}^2}{3y^2+6y-1y-2}\\ =\frac{{\left(y+2\right)}^2}{3y\left(y+2\right)-1\left(y+2\right)}\\ =\frac{{\left(y+2\right)}^2}{\left(3y-1\right)\left(y+2\right)}\\ =\frac{y+2}{3y-1}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{y+2}{3y-1}$.