Question

Answer 1

a: ĐKXĐ: x>0; x<>1

b: \(P=\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\right):\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}+1}\right)\)

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

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

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

c: Thay x=4 vào P, ta được:

\(P=\frac{2+1}{2\cdot2}=\frac34\)