Question

Bài tập:Rút gọn biểu thức

P=\(\left(\dfrac{1}{2\sqrt{a}-a}+\dfrac{1}{2-\sqrt{a}}\right):\dfrac{\sqrt{a}+1}{a-2\sqrt{a}}\)với a>0 và a\(\ne\)4

Answer 1

P = \(\left(\dfrac{1}{2\sqrt{a}-a}+\dfrac{1}{2-\sqrt{a}}\right):\dfrac{\sqrt{a}+1}{a-2\sqrt{a}}\) (a > 0; a \(\ne\) 4)

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

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

P = -1

Vậy P = -1 với a > 0; a \(\ne\) 4

Chúc bn học tốt!

Answer 2

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

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

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

\(=\dfrac{1}{-1}=-1\)