Answer
$x=9$
Work Step by Step
We are given:
$\sqrt{x}-\sqrt{x-5}=1$
$\sqrt{x}=1+\sqrt{x-5}$
We square both sides:
$(\sqrt{x})^{2}=(1+\sqrt{x-5})^{2}$
$(\sqrt{x})^{2}=(1+\sqrt{x-5})(1+\sqrt{x-5})$
We distribute:
$x=1+2\sqrt{x-5}+(x-5)$
And combine like terms:
$0=-4+2\sqrt{x-5}$
$4=2\sqrt{x-5}$
$2=\sqrt{x-5}$
We square both sides again:
$2^{2}=(\sqrt{x-5})^{2}$
$4=x-5$
And solve for $x$:
$x=9$