Question

1. cho biểu thức

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

a, rút gọn bt a

 

Answer 1

Lời giải:

ĐKXĐ: $a\geq 0; a\neq 4$

\(A=\left[\frac{\sqrt{a}(\sqrt{a}-2)-\sqrt{a}(\sqrt{a}+2)}{(\sqrt{a}+2)(\sqrt{a}-2)}+\frac{4\sqrt{a}-1}{(\sqrt{a}-2)(\sqrt{a}+2)}\right].(\sqrt{a}+2)\)

\(=\frac{-4\sqrt{a}+4\sqrt{a}-1}{(\sqrt{a}-2)(\sqrt{a}+2)}.(\sqrt{a}+2)=\frac{-1}{(\sqrt{a}-2)(\sqrt{a}+2)}.(\sqrt{a}+2)=\frac{1}{2-\sqrt{a}}\)