a: \(=\dfrac{44x+52-45x-51}{12\left(x-1\right)}=\dfrac{-x+1}{12\left(x-1\right)}=\dfrac{-1}{12}\)
b: \(=\dfrac{2x+1}{x\left(2x-1\right)}-\dfrac{32x^2}{\left(2x-1\right)\left(2x+1\right)}+\dfrac{1-2x}{x\left(2x+1\right)}\)
\(=\dfrac{4x^2+4x+1-32x^2-4x^2+4x-1}{x\left(2x-1\right)\left(2x+1\right)}=\dfrac{-32x^2+8x}{x\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{-8x\left(4x^2-1\right)}{x\left(2x-1\right)\left(2x+1\right)}=-8\)
c: \(=\dfrac{1}{x^2+x+1}+\dfrac{1}{x\left(x-1\right)}-\dfrac{2x}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2-x+x^2+x+1-2x^2}{x\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x\left(x-1\right)\left(x^2+x+1\right)}\)
d: \(=\dfrac{3x+5}{x\left(x-5\right)}+\dfrac{x-25}{5\left(x-5\right)}\)
\(=\dfrac{15x+25+x^2-25x}{5x\left(x-5\right)}=\dfrac{\left(x-5\right)^2}{5x\left(x-5\right)}=\dfrac{x-5}{5x}\)
