To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $4a^{2}-g$ and $2a-3$ is $\left(2a-3\right)\left(4a^{2}-g\right)$. Multiply $\frac{4a^{2}+12a+9}{4a^{2}-g}$ times $\frac{2a-3}{2a-3}$. Multiply $\frac{a+2}{2a-3}$ times $\frac{4a^{2}-g}{4a^{2}-g}$.
Since $\frac{\left(4a^{2}+12a+9\right)\left(2a-3\right)}{\left(2a-3\right)\left(4a^{2}-g\right)}$ and $\frac{\left(a+2\right)\left(4a^{2}-g\right)}{\left(2a-3\right)\left(4a^{2}-g\right)}$ 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 $4a^{2}-g$ and $2a-3$ is $\left(2a-3\right)\left(4a^{2}-g\right)$. Multiply $\frac{4a^{2}+12a+9}{4a^{2}-g}$ times $\frac{2a-3}{2a-3}$. Multiply $\frac{a+2}{2a-3}$ times $\frac{4a^{2}-g}{4a^{2}-g}$.
Since $\frac{\left(4a^{2}+12a+9\right)\left(2a-3\right)}{\left(2a-3\right)\left(4a^{2}-g\right)}$ and $\frac{\left(a+2\right)\left(4a^{2}-g\right)}{\left(2a-3\right)\left(4a^{2}-g\right)}$ have the same denominator, subtract them by subtracting their numerators.
