\(a,\dfrac{x+3}{xy+3y}+\dfrac{5x^2-5xy}{y\left(x-y\right)}=\dfrac{x+3}{y\left(x+3\right)}+\dfrac{5x\left(x-y\right)}{y\left(x-y\right)}=\dfrac{1}{y}+\dfrac{5x}{y}=\dfrac{5x+1}{y}\)
\(b,\left(\dfrac{2x}{x-1}-\dfrac{2x^2+x}{x^2+x+1}\right):\dfrac{x+1}{x^3-1}=\dfrac{2x\left(x^2+x+1\right)-\left(2x^2+x\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}.\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{x+1}=\dfrac{2x^3+2x^2+2x-2x^3-x^2+2x^2+x}{x+1}=\dfrac{3x^2+3x}{x+1}=\dfrac{3x\left(x+1\right)}{x+1}=3x\)
a: \(=\dfrac{x+3}{y\left(x+3\right)}+\dfrac{5x\left(x-y\right)}{y\left(x-y\right)}=\dfrac{1+5x}{y}\)
b: \(=\dfrac{2x^3+2x^2+2x-x\left(2x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^3-1}{x+1}\)
\(=\dfrac{2x^3+2x^2+2x-x\left(2x^2-2x+x-1\right)}{x+1}\)
\(=\dfrac{2x^3+2x^2+2x-2x^3+x^2+x}{\left(x+1\right)}=\dfrac{3x^3+3x}{x+1}=3x\)
