Question

Tính P = \(\frac{1}{\sqrt{x}+1}+\frac{2}{\sqrt{x}-1}-\frac{4}{x-1}\)

Answer 1

ĐKXĐ: \(x>1\)

\(P=\frac{1}{\sqrt{x}+1}+\frac{2}{\sqrt{x}-1}-\frac{4}{x-1}\)

\(P=\frac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}+\frac{2\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\frac{4}{x-1}\)

\(P=\frac{\sqrt{x}-1}{x-1}+\frac{2\sqrt{x}+2}{x-1}-\frac{4}{x-1}\)

\(P=\frac{3\sqrt{x}+1-4}{x-1}=\frac{3\sqrt{x}-3}{x-1}=\frac{3\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{3}{\sqrt{x}+1}\)