a: \(=\dfrac{5}{2x\left(x+3\right)}+\dfrac{3x^2-4}{\left(x-3\right)\left(x+3\right)}-3\)
\(=\dfrac{5x-15+2x\left(3x^2-4\right)-6x\left(x+3\right)\left(x-3\right)}{2x\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{\left(5x-15+6x^3-8x-6x^3+54x\right)}{2x\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{51x-15}{2x\left(x+3\right)\left(x-3\right)}\)
d: \(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x-2y\right)\left(x+2y\right)}=\dfrac{2x^2-4xy}{\left(x-2y\right)\left(x+2y\right)}=\dfrac{2x}{x+2y}\)
e: \(=\dfrac{\left(-3x+1\right)\left(2x-1\right)+6x^2-4x-3x+2}{2x\left(2x-1\right)}\)
\(=\dfrac{-6x^2+3x+2x-1+6x^2-7x+2}{2x\left(2x-1\right)}\)
\(=\dfrac{-2x+1}{2x\left(2x-1\right)}=\dfrac{-1}{2x}\)
