Question

Someone please help me with number 6. Also show your work as that will help a lot

Answer 1

$\bf f(x) = x^2+3x+9 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x+h)^2+3(x+h)+9~~~~-~~~~(x^2+3x+9)}{h} \\\\\\ \cfrac{(x+h)^2+3(x+h)+9~~~~~~-x^2-3x-9}{h} \\\\\\ \cfrac{\stackrel{F~~O~~I~~L}{(x^2+2hx+h^2)}+3x+3h+9~~~~~~-x^2-3x-9}{h}$

$\bf \cfrac{(2hx+h^2+3h)~~\begin{matrix} +x^2-x^2+3x-3x+9-9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{h}\implies \cfrac{\stackrel{\textit{common factor}}{~~\begin{matrix} h \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(2x+h+3)}}{~~\begin{matrix} h \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 2x+h+3~\hfill$