Question

Cho biểu thức A=\(\frac{\left(\sqrt{a}+\sqrt{b}\right)^2-4\sqrt{ab}}{\sqrt{a}-\sqrt{b}}-\frac{a\sqrt{b}+b\sqrt{a}}{\sqrt{ab}}\)

a)Tìm ĐKXĐ

b)Rút gọn A

Answer 1

a)ĐKXĐ: \(\left\{{}\begin{matrix}\sqrt{a}\ge0\\\sqrt{b}\ge0\\\sqrt{a}-\sqrt{b}\ne0\\\sqrt{ab}\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a>0\\b>0\\a\ne b\end{matrix}\right.\)

b)\(A=\frac{\left(\sqrt{a}+\sqrt{b}\right)^2-4\sqrt{ab}}{\sqrt{a}-\sqrt{b}}-\frac{a\sqrt{b}+b\sqrt{a}}{\sqrt{ab}}\)

\(=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}}\)

\(=\sqrt{a}-\sqrt{b}-\sqrt{a}-\sqrt{b}\)

\(=-2\sqrt{b}\)