\(a,=\dfrac{\left(3x-1\right)\left(x+3\right)-\left(x-1\right)\left(2x+5\right)-2\left(x+1\right)}{\left(x-1\right)\left(x+3\right)}\left(1-x\right)\\ =\dfrac{3x^2+8x-3-2x^2-3x+5-2x-2}{\left(x-1\right)\left(x+3\right)}\left(1-x\right)\\ =\dfrac{x\left(x+3\right)\left(1-x\right)}{x\left(x-1\right)\left(x+3\right)}=-x\)
\(b,=\dfrac{3x+9+x^2+x-2-x-7}{\left(x-1\right)\left(x+3\right)}\left(1-x\right)=\dfrac{x\left(x+3\right)\left(1-x\right)}{\left(x-1\right)\left(x+3\right)}=-x\)
\(c,=\dfrac{3x^2+x^2-1}{x\left(x-1\right)}\cdot\dfrac{x-1}{2x+1}=\dfrac{\left(2x-1\right)\left(2x+1\right)}{x\left(x-1\right)}\cdot\dfrac{x-1}{2x+1}=\dfrac{2x-1}{x}\)
\(d,=\dfrac{3x^2-5x-2-x^2-2x+7x}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{\left(x-2\right)\left(x+2\right)}{2}\\ =\dfrac{2\left(x^2-1\right)}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{\left(x-2\right)\left(x+2\right)}{2}=x^2-1\)
