a: \(\dfrac{x^2+y^2}{x-y}+\dfrac{2xy}{y-x}\)
\(=\dfrac{x^2+y^2}{x-y}-\dfrac{2xy}{x-y}\)
\(=\dfrac{x^2-2xy+y^2}{x-y}=\dfrac{\left(x-y\right)^2}{x-y}=x-y\)
b: ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
\(\left(\dfrac{x+2}{x+1}-\dfrac{x}{x-1}\right)\cdot\dfrac{3x+3}{2}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)-x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{3\left(x+1\right)}{2}\)
\(=\dfrac{x^2+x-2-x^2-x}{\left(x-1\right)}\cdot\dfrac{3}{2}\)
\(=\dfrac{-2}{x-1}\cdot\dfrac{3}{2}=\dfrac{-3}{x-1}\)
c: ĐKXĐ: \(x\notin\left\{5;-5;-1\right\}\)
\(\left(\dfrac{4}{x-5}-\dfrac{1}{x+5}+\dfrac{13x-x^2}{25-x^2}\right):\dfrac{x+1}{2x+10}\)
\(=\left(\dfrac{4}{x-5}-\dfrac{1}{x+5}+\dfrac{x^2-13x}{\left(x-5\right)\left(x+5\right)}\right)\cdot\dfrac{2\left(x+5\right)}{x+1}\)
\(=\dfrac{4\left(x+5\right)-x+5+x^2-13x}{\left(x-5\right)\left(x+5\right)}\cdot\dfrac{2\left(x+5\right)}{x+1}\)
\(=\dfrac{4x+20+x^2-14x+5}{x-5}\cdot\dfrac{2}{x+1}\)
\(=\dfrac{x^2-10x+25}{x-5}\cdot\dfrac{2}{x+1}=\dfrac{\left(x-5\right)^2\cdot2}{\left(x-5\right)\left(x+1\right)}=\dfrac{2\left(x-5\right)}{x+1}\)
