Question

If =" g(x)=\frac{1}{x} " align="absmiddle" class="latex-formula"> and $h$ is a nonzero real number, then $\frac{g(x+h)-g(x)}{h}=$

Answer 1

Fill in the given values and simplify.

$\dfrac{g(x+h)-g(x)}{h}=\dfrac{\dfrac{1}{x+h}-\dfrac{1}{x}}{h}\\\\=\dfrac{x-(x+h)}{h\cdot x(x+h)}\\\\=\dfrac{-1}{x(x+h)}$