11) \(\dfrac{x+2}{2x-4}-\dfrac{4x}{x^2-4}\) (ĐK: \(x\ne\pm2\))
\(=\dfrac{x+2}{2\left(x-2\right)}-\dfrac{4x}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{\left(x+2\right)^2}{2\left(x-2\right)\left(x+2\right)}-\dfrac{8x}{2\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x^2+4x+4-8x}{2\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x^2-4x+4}{2\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{\left(x-2\right)^2}{2\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x-2}{2\left(x+2\right)}\)
12) \(\dfrac{x}{x-1}-\dfrac{5x-3}{x^2-1}\) (ĐK: \(x\ne\pm1\))
\(=\dfrac{x}{x-1}-\dfrac{5x-3}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\dfrac{5x-3}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+x-5x+3}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2-4x+3}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2-x-3x+3}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\left(x-1\right)\left(x-3\right)}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x-3}{x+1}\)
