Question

[Sam Nguyễn]

Bài 1: Cho biểu thức:
B= \(\dfrac{a\sqrt{a}-1}{a-\sqrt{a}}-\dfrac{a\sqrt{a}+1}{a+\sqrt{a}}\)+(\(1-\dfrac{1}{\sqrt{a}}\)) (\(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}+\dfrac{\sqrt[]{a}-1}{\sqrt{a}+1}\)) 

Rút gọn B

Answer 1

[Nguyễn Lê Phước Thịnh]

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

\(=2+\dfrac{1}{\sqrt{a}}\cdot\dfrac{2a+2}{\sqrt{a}+1}\)

\(=\dfrac{2a+2\sqrt{a}+2a+2}{\sqrt{a}\left(\sqrt{a}+1\right)}=\dfrac{4a+2\sqrt{a}+2}{\sqrt{a}\left(\sqrt{a}+1\right)}\)