Question

rút gọn \(\left(\frac{1}{2\sqrt{a}-a}+\frac{1}{2-\sqrt{a}}\right):\frac{\sqrt{a}+1}{a-2\sqrt{a}}+\frac{\sqrt{a}}{a+2}\) với a lớn hơn 0 và a khác 4 các bạn giúp mình với ạ

Answer 1

ĐKXĐ : \(\left\{{}\begin{matrix}a\ge0\\a\ne4\end{matrix}\right.\)

Ta có :

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

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

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

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

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

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