What are the steps they're using to simplify this?

Answer: Distribute, Combine like terms, factor, & simplify
Step-by-step explanation:
[tex].\quad \dfrac{(x+h)^2+9(x+h)-(x^2+9x)}{h}\\\\=\dfrac{x^2+2xh+h^2+9x+9h-x^2-9x}{h}\quad \rightarrow\ \text{Distributed}\\\\=\dfrac{2xh+h^2+9h}{h}\quad \rightarrow\ \text{Combined like terms}\\\\=\dfrac{h(2x+h+9)}{h}\quad \rightarrow\ \text{Factored}\\\\=2x+h+9\quad \rightarrow\ \text{Simplified}[/tex]