\(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4x}{x^2-1}\)
\(\Leftrightarrow\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}-\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}=\frac{4x}{\left(x-1\right)\left(x+1\right)}\)
\(\Leftrightarrow\frac{\left(x+1\right)^2-\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}=\frac{4x}{\left(x-1\right)\left(x+1\right)}\)
\(\Leftrightarrow\left(x+1\right)^2-\left(x-1\right)^2=4x\)
\(\Leftrightarrow x^2+2x+1-\left(x^2-2x+1\right)-4x=0\)
\(\Leftrightarrow x^2+2x+1-x^2+2x-1-4x=0\)
\(\Leftrightarrow0=0\)( luôn đúng )
Vậy pt đúng với mọi x là số thực
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