Answer
$ \frac{x+\sqrt {x^2-h^2}}{h}$
Work Step by Step
$\frac{\sqrt {x+h}+\sqrt {x-h}}{\sqrt {x+h}-\sqrt {x-h}}=\frac{\sqrt {x+h}+\sqrt {x-h}}{\sqrt {x+h}-\sqrt {x-h}}\times\frac{\sqrt {x+h}+\sqrt {x-h}}{\sqrt {x+h}+\sqrt {x-h}}=\frac{x+h+2\sqrt {x+h}\sqrt {x-h} +x-h}{x+h-x+h}=\frac{x+\sqrt {x^2-h^2}}{h}$
