Question 258224
Solve for x:
{{{sqrt(x)-sqrt(x-5) = 1}}} Add {{{sqrt(x-5)}}} to both sides.
{{{sqrt(x) = sqrt(x-5)+1}}} square both sides.
{{{(sqrt(x))^2 = (sqrt(x-5)+1)^2}}} 
{{{x = (x-5)+2*sqrt(x-5)+1}}} Simplify.
{{{x = x-4+2sqrt(x-5)}}} Add 4 to both sides.
{{{x+4 = x+2sqrt(x-5)}}} Subtract x from both sides.
{{{4 = 2sqrt(x-5)}}} Divide both sides by 2.
{{{2 = sqrt(x-5)}}} Square both sides.
{{{4 = x-5}}} Add 5 to both sides.
{{{9 = x}}} or {{{highlight(x = 9)}}}
Check:
{{{sqrt(x)-sqrt(x-5) = 1}}} Substitute x = 9.
{{{sqrt(9)-sqrt(9-5) = 1}}} Evaluate.
{{{3-2 = 1}}}