Question

Rút gọn biểu thức:

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

Answer 1

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

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

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