a) \(\dfrac{7}{8x^2-18}+\dfrac{1}{2x^2+3x}-\dfrac{1}{4x-6}\)
\(=\dfrac{7}{2\left(4x^2-9\right)}+\dfrac{1}{x\left(2x+3\right)}-\dfrac{1}{2\left(2x-3\right)}\)
\(=\dfrac{7}{2\left(2x-3\right)\left(2x+3\right)}+\dfrac{1}{x\left(2x+3\right)}-\dfrac{1}{2\left(2x-3\right)}\) MTC: \(2x\left(2x-3\right)\left(2x+3\right)\)
\(=\dfrac{7x}{2x\left(2x-3\right)\left(2x+3\right)}+\dfrac{2\left(2x-3\right)}{2x\left(2x-3\right)\left(2x+3\right)}-\dfrac{x\left(2x+3\right)}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{7x+2\left(2x-3\right)-x\left(2x+3\right)}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{7x+\left(4x-6\right)-\left(2x^2+3x\right)}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{7x+4x-6-2x^2-3x}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2x^2+8x-6}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2\left(x^2-4x+3\right)}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2\left(x^2-x-3x+3\right)}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2\left[\left(x^2-x\right)-\left(3x-3\right)\right]}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2\left[x\left(x-1\right)-3\left(x-1\right)\right]}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2\left(x-1\right)\left(x-3\right)}{2x\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-\left(x-1\right)\left(x-3\right)}{x\left(2x-3\right)\left(2x+3\right)}\)
