Question

Đơn giản các biểu thức sau :

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

Answer 1

\(=\left(\sqrt{a}-\sqrt{b}\right)^2:\left(\sqrt{b}-\frac{b}{\sqrt{a}}\right)^2=\left(\sqrt{a}-\sqrt{b}\right)^2:\left[\frac{\sqrt{b}}{\sqrt{a}}\left(\sqrt{a}-\sqrt{b}\right)\right]^2\)

\(=\left(\sqrt{a}-\sqrt{b}\right)^2:\left[\frac{\sqrt{b}}{\sqrt{a}}\left(\sqrt{a}-\sqrt{b}\right)\right]^2\)

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