Question

\(\dfrac{1}{\sqrt{a}+1}\)- \(\dfrac{-2\sqrt{a}}{a\sqrt{a}+\sqrt{a}+a+1}\)

Answer 1

\(\dfrac{1}{\sqrt{a}+1}-\dfrac{-2\sqrt{a}}{a\sqrt{a}+\sqrt{a}+a+1}=\dfrac{1}{\sqrt{a}+1}-\dfrac{-2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}+1\right)}\\ =\dfrac{a+1+2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}+1\right)}=\dfrac{\left(\sqrt{a}+1\right)^2}{\left(a+1\right)\left(\sqrt{a}+1\right)}\\ =\dfrac{\sqrt{a}+1}{a+1}\)

Answer 2

\(\dfrac{a+1}{\left(a+1\right)\left(\sqrt{a}+1\right)}-\dfrac{-2\sqrt{a}}{\sqrt{a}\left(a+1\right)+\left(a+1\right)}\)