Answer
a. $\quad h(2x+1+h)$
b. $\quad 2x+1+h$
Work Step by Step
a.
$ f(x+h)=(x+h)^{2}+(x+h)=\quad$ ...square of a sum
$=x^{2}+2xh+h^{2}+x+h$
$f(x+h)-f(x)=x^{2}+2xh+h^{2}+x+h-(x^{2}+x)$
$=x^{2}+2xh+h^{2}+x+h-x^{2}-x$
$=2xh+h+h^{2}$
$=h(2x+1+h)$
b.
using the result of (a),
$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{h(2x+1+h)}{h}=\quad$ .. reduce h,
$=2x+1+h$
