Question

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

Answer 1

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

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

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

4x-2-x²+2x=x²+2x-2x-4-2x²+4x

4x+2x-2x+2x-4x-x²-x²+2x²=2-4

2x=-2

x=\(\frac{-2}{2}\)

x=-1