Answer
$$\frac{4x^2-9}{4x^2+12x+9}=\frac{2x-3}{2x+3}$$
Explanation
| $$ \begin{aligned}\frac{4x^2-9}{4x^2+12x+9}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2x-3}{2x+3}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{4x^2-9}{4x^2+12x+9} $ to $ \dfrac{2x-3}{2x+3} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{2x+3}$. $$ \begin{aligned} \frac{4x^2-9}{4x^2+12x+9} & =\frac{ \left( 2x-3 \right) \cdot \color{blue}{ \left( 2x+3 \right) }}{ \left( 2x+3 \right) \cdot \color{blue}{ \left( 2x+3 \right) }} = \\[1ex] &= \frac{2x-3}{2x+3} \end{aligned} $$ |
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Simplify Rational Expressions