$$\frac { x } { 2 x + 3 } + \frac { x } { 2 x - 3 } - \frac { 9 } { 4 x ^ { 2 } - 9 }$$
Evaluate
$1$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2x+3$ and $2x-3$ is $\left(2x-3\right)\left(2x+3\right)$. Multiply $\frac{x}{2x+3}$ times $\frac{2x-3}{2x-3}$. Multiply $\frac{x}{2x-3}$ times $\frac{2x+3}{2x+3}$.
Since $\frac{x\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}$ and $\frac{x\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{4x^{2}}{\left(2x-3\right)\left(2x+3\right)}$ and $\frac{9}{\left(2x-3\right)\left(2x+3\right)}$ have the same denominator, subtract them by subtracting their numerators.
