Question

\(\left(\frac{x+1}{x}\right)^2-\left(\frac{x}{x+1}\right)^2=\frac{3}{2}\)

Answer 1

ĐKXĐ: \(x\ne0;-1\)

Đặt \(\left(\frac{x+1}{x}\right)^2=a>0\) phương trình trở thành:

\(a-\frac{1}{a}=\frac{3}{2}\Leftrightarrow2a^2-3a-2=0\Rightarrow\left[{}\begin{matrix}a=2\\a=\frac{-1}{2}\left(l\right)\end{matrix}\right.\)

\(\Rightarrow\left(\frac{x+1}{x}\right)^2=2\Leftrightarrow\left(x+1\right)^2=2x^2\Leftrightarrow x^2-2x-1=0\) \(\Rightarrow\left[{}\begin{matrix}x=1-\sqrt{2}\\x=1+\sqrt{2}\end{matrix}\right.\)