a: \(=\dfrac{3\left(2x+4\right)+2\left(2-x\right)}{30}=\dfrac{6x+12+4-2x}{30}=\dfrac{4x+16}{30}=\dfrac{2x+8}{15}\)
b: \(=\dfrac{18x}{60}+\dfrac{8x-8}{60}+\dfrac{6-3x}{60}\)
\(=\dfrac{18x+8x-8+6-3x}{60}=\dfrac{23x-2}{60}\)
c: \(=\dfrac{x+1}{2\left(x-1\right)}-\dfrac{x^2+3}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+2x+1-x^2-3}{2\left(x-1\right)\left(x+1\right)}=\dfrac{2x-2}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x+1}\)
d: \(=\dfrac{-\left(2x-1\right)^2+4x^2-1}{2x\left(2x-1\right)}=\dfrac{-4x^2+4x-1+4x^2-1}{2x\left(2x-1\right)}\)
\(=\dfrac{4x-2}{x\left(4x-2\right)}=\dfrac{1}{x}\)
e: \(=\dfrac{x}{y\left(x-y\right)}+\dfrac{2x-y}{x\left(y-x\right)}\)
\(=\dfrac{x^2-2xy+y^2}{xy\left(x-y\right)}=\dfrac{\left(x-y\right)^2}{xy\left(x-y\right)}=\dfrac{x-y}{xy}\)
