If $LaTeX: \displaystyle f(x)=5 - 8 x$ and $LaTeX: \displaystyle g(x)=\frac{2 x + 3}{9 x^{2} + 7 x - 4}$ find $LaTeX: \displaystyle (f\circ g)(x)$ .

Evaluating $LaTeX: \displaystyle f(x)$ at $LaTeX: \displaystyle g(x)$ gives $LaTeX: \displaystyle (f\circ g)(x)=f(g(x))=- \frac{8 \left(2 x + 3\right)}{9 x^{2} + 7 x - 4} + 5$ .