Question

Simplify {1/[sqrt(a) + sqrt(a+1)] + [ 1/[sqrt(a) - sqrt(a-1)]} : {1+sqrt[(a+1)/(a-1)]} .

Answer 1

\[\frac{1}{\sqrt{a}+\sqrt{a+1}} +\frac{1}{\sqrt{a}-\sqrt{a-1}}\]
\[\frac{1}{\sqrt{a}+\sqrt{a+1}} \cdot \frac{\sqrt{a}-\sqrt{a+1}}{\sqrt{a}-\sqrt{a+1}}+\frac{1}{\sqrt{a}-\sqrt{a-1}} \cdot \frac{\sqrt{a}+\sqrt{a-1}}{\sqrt{a}+\sqrt{a-1}}\]
\[\frac{\sqrt{a}-\sqrt{a+1}}{a-(a+1)} +\frac{\sqrt{a}+\sqrt{a-1}}{a-(a-1)}\]
\[\frac{\sqrt{a}-\sqrt{a+1}}{-1}+\frac{\sqrt{a}+\sqrt{a-1}}{1}\]
\[-\sqrt{a}+\sqrt{a+1}+\sqrt{a}+\sqrt{a-1}=\sqrt{a-1}+\sqrt{a+1}\]

Answer 2

i didn't know what that last part was for that you have?

Answer 3

I got that last one myself . Thanks again !