a: \(=\dfrac{3y}{2x^2y^2}+\dfrac{10x}{2x^2y^2}+\dfrac{x}{y^3}=\dfrac{10x+3y}{2x^2y^2}+\dfrac{x}{y^3}\)
\(=\dfrac{10xy+3y^2+2x^3}{2x^2y^3}\)
b: \(=\dfrac{x^3-1}{x-1}+\dfrac{-x^2+1}{x+1}\)
\(=x^2+x+1-x+1=x^2+2\)
c: \(=\dfrac{x^2+2xy+y^2-x^2+2xy-y^2+4y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{4y^2+4xy}{2\left(x-y\right)\left(x+y\right)}=\dfrac{4y\left(x+y\right)}{2\left(x-y\right)\left(x+y\right)}=\dfrac{2y}{x-y}\)
d: \(=\dfrac{x+5}{2x-4}\cdot\dfrac{-\left(2x-4\right)}{x+2}=\dfrac{-x-5}{x+2}\)
e: \(=\dfrac{8+2x-2+x+3}{\left(x+3\right)\left(x-1\right)}=\dfrac{3x+9}{\left(x+3\right)\left(x-1\right)}=\dfrac{3}{x-1}\)
f: \(=\dfrac{4x^2-1}{x\left(x+4\right)}\cdot\dfrac{3x}{2\left(2x-1\right)}\)
\(=\dfrac{\left(2x-1\right)\left(2x+1\right)}{2\left(2x-1\right)}\cdot\dfrac{3}{x+4}=\dfrac{3}{x+4}\cdot\dfrac{2x+1}{2}=\dfrac{6x+3}{2x+8}\)
