To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-2\right)\left(x+2\right)$ and $x+2$ is $\left(x-2\right)\left(x+2\right)$. Multiply $\frac{1}{x+2}$ times $\frac{x-2}{x-2}$.
Since $\frac{5x+6}{\left(x-2\right)\left(x+2\right)}$ and $\frac{x-2}{\left(x-2\right)\left(x+2\right)}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-2\right)\left(x+2\right)$ and $x+2$ is $\left(x-2\right)\left(x+2\right)$. Multiply $\frac{1}{x+2}$ times $\frac{x-2}{x-2}$.
Since $\frac{5x+6}{\left(x-2\right)\left(x+2\right)}$ and $\frac{x-2}{\left(x-2\right)\left(x+2\right)}$ have the same denominator, subtract them by subtracting their numerators.
