Question

Cho biểu thức 

M= \(\left(\frac{\sqrt{x}+3}{\sqrt{x}-3}-\frac{\sqrt{x}-3}{\sqrt{x}+3}\right)\) : \(\left(\frac{\sqrt{x}}{\sqrt{x}+3}-1\right)\)

a, Rút gọn

b, Tìm x để M có gtrị dương

Answer 1

\(M=\left(\frac{\sqrt{x}+3}{\sqrt{x}-3}-\frac{\sqrt{x}-3}{\sqrt{x}+3}\right):\left(\frac{\sqrt{x}}{\sqrt{x}+3}-1\right)\)  ĐKXĐ : \(x\ge0;x\ne-3;x\ne3\)

\(M=\frac{\left(\sqrt{x}+3\right)^2-\left(\sqrt{x}-3\right)^2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}:\frac{\sqrt{x}-\sqrt{x}-3}{\sqrt{x}-3}\)

\(M=\frac{x+6\sqrt{x}+9-x+6\sqrt{x}-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}.\frac{\sqrt{x}-3}{-3}\)

\(M=\frac{12\sqrt{x}}{\sqrt{x}+3}.\frac{1}{-3}\)

\(M=\frac{-4\sqrt{x}}{\sqrt{x}+3}\)