Question

M = \(\frac{1}{\sqrt{x}}\)+\(\frac{\sqrt{x}}{\sqrt{x}+1}\), N = \(\frac{\sqrt{x}}{x+\sqrt{x}}\)

TÍNH S=M : N

HELP ME PLSSS

Answer 1

ĐKXĐ: \(x>0\)

\(S=\left(\frac{1}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+1}\right)\div\left(\frac{\sqrt{x}}{x+\sqrt{x}}\right)=\left(\frac{1}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+1}\right)\left(\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}}\right)\)

\(=\left(\frac{1}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+1}\right)\left(\sqrt{x}+1\right)=\frac{\sqrt{x}+1}{\sqrt{x}}+\sqrt{x}=\frac{x+\sqrt{x}+1}{\sqrt{x}}\)