Question

\(A=\left(\frac{1}{\sqrt{x}+3}-\frac{4}{9-x}\right).\frac{2\sqrt{x}-6}{\sqrt{x}+1}\)  với \(x\ge0;x\ne9\)

a) rút gọn và CMR \(A=\frac{2}{\sqrt{x}+3}\)

Answer 1

a) \(A=\left(\frac{1}{\sqrt{x}+3}-\frac{4}{9-x}\right).\frac{2\sqrt{x}-6}{\sqrt{x}+1}\)

\(A=\left[\frac{\sqrt{x}-3}{x-9}+\frac{4}{x-9}\right].\frac{2\left(\sqrt{x}-3\right)}{\sqrt{x}+1}\)

\(A=\frac{\sqrt{x}-3+4}{x-9}.\frac{2\left(\sqrt{x}-3\right)}{\sqrt{x}+1}\)

\(A=\frac{\sqrt{x}+1}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\frac{2\left(\sqrt{x}-3\right)}{\sqrt{x}+1}\)

\(A=\frac{2}{\sqrt{x}+3}\)   

vậy \(A=\frac{2}{\sqrt{x}+3}\)