Question

Cho biểu thức:

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

rút gọn biểu thức

Answer 1

ĐKXĐ:...

\(A=\left(\frac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+\frac{a}{\sqrt{a}\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right):\left(\frac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)^2}\right)\)

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