Question

Simplify: \frac{ 1 }{ sqrt{2}-sqrt{x+2} } so that there are no radicals in the denominator

Answer 1

\[\frac{ 1 }{ \sqrt{2} + \sqrt{x+2} }\] I thought that I needed to multiply the function by the denominator's reciprocal of: \[\frac{ \sqrt{2}-\sqrt{x+2} }{\sqrt{2}-\sqrt{x+2} }\]When I worked that through I ended up with a solution of: \[\frac{ \sqrt{2}-\sqrt{x+2} }{ 4-x }\] not the answer of: \[\frac{ \sqrt{2}-\sqrt{x+2} }{ x }\]
Can someone work through this with me?

Answer 2

Sorry, wrong answer typed there it should say they got: \[\frac{ \sqrt{x+2}-\sqrt{2} }{ x }\]