Question

Simplify the expression$\frac{a^2+2a+1}{2a^2+3a+1}$

Short answer

The simplified value of expression is$\frac{a+1}{2a+1}$

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{a^2+2a+1}{2a^2+3a+1}$

Step 2. Simplify the expression.

The given expression $\frac{a^2+2a+1}{2a^2+3a+1}$is simplified as:

$\begin{array}{c}\frac{a^2+2a+1}{2a^2+3a+1}=\frac{{\left(a+1\right)}^2}{2a^2+2a+a+1}\\ =\frac{{\left(a+1\right)}^2}{2a\left(a+1\right)+1\left(a+1\right)}\\ =\frac{{\left(a+1\right)}^2}{\left(2a+1\right)\left(a+1\right)}\\ =\frac{a+1}{2a+1}\end{array}$

Step 3. Conclusion.

The simplified value of expression is$\frac{a+1}{2a+1}$