Question

Cho biểu thức

P= \(\left(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}\right).\left(\frac{\sqrt{x}-1}{7}\right)\)

a. rút gọn P

b, tìm x để P=4

Answer 1

a) Ta có: \(P=\left(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}\right)\cdot\left(\frac{\sqrt{x}-1}{7}\right)\)

\(=\left(\frac{x+2+\sqrt{x}\left(\sqrt{x}-1\right)-\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\cdot\frac{\sqrt{x}-1}{7}\)

\(=\frac{x+2+x-\sqrt{x}-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\frac{\sqrt{x}-1}{7}\)

\(=\frac{x-2\sqrt{x}+1}{x+\sqrt{x}+1}\cdot\frac{1}{7}\)

\(=\frac{\left(\sqrt{x}-1\right)^2}{7\left(x+\sqrt{x}+1\right)}\)