TeX source:

\begin{aligned}\frac{f(a+h)-f(a)}{h} &=\frac{\left(a^{2}+2 a h+h^{2}+3 a+3 h-4\right)-\left(a^{2}+3 a-4\right)}{h}\\&=\frac{2 a h+h^{2}+3 h}{h}\\&=\frac{h(2 a+h+3)}{h} \qquad \qquad \text { Factor out } h \text {. }\\&=2 a+h+3 \qquad \qquad \qquad \text { Simplify. }\end{aligned}