Question

CMR: \(P=\frac{x}{x+1}+\frac{x}{x-1}+\frac{2x^2}{1-x^2}\) không phụ thuộc vào x

Answer 1

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

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

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

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

\(=0\)

\(\Leftrightarrow P\) không phụ thuộc vào x \(\left(đpcm\right)\)

Answer 2

https://i.imgur.com/xiefnEQ.jpg