Question

rút gọn biểu thức: P=\(\frac{1}{1-\sqrt{a}}+\frac{a\sqrt{a}}{\sqrt{a}-1}\)

và tính P với a=\(\frac{1}{4}\)

Answer 1

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

Answer 2

Với a = 1/4 thì:
\(P=\frac{a\sqrt{a}-1}{\sqrt{a}-1}=\frac{\frac{1}{4}\sqrt{\frac{1}{4}}-1}{\sqrt{\frac{1}{4}}-1}=\frac{\frac{1}{4}\cdot\frac{1}{2}-1}{\frac{1}{2}-1}=\frac{\frac{1}{8}-1}{\frac{1}{2}-1}=\frac{1-\frac{1}{8}}{1-\frac{1}{2}}=\frac{\frac{7}{8}}{\frac{1}{2}}=\frac{7}{4}\)

Answer 3

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

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