Question

rút gọn:\(\left(1+\dfrac{\sqrt{a}}{a-1}\right)/\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{a\sqrt{a}+\sqrt{a}-a-1}\right)\)

Answer 1

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

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

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

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