\(\dfrac{x}{2x^2+7x-15}=\dfrac{x}{\left(x+5\right)\left(2x-3\right)}=\dfrac{x\left(x-2\right)}{\left(x+5\right)\left(2x-3\right)\left(x-2\right)}\)
\(\dfrac{x+2}{x^2+3x-10}=\dfrac{\left(x+2\right)\left(2x-3\right)}{\left(x+5\right)\left(2x-3\right)\left(x-2\right)}\)
\(\dfrac{1}{x+5}=\dfrac{\left(2x-3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-3\right)\left(x-2\right)}\)
b: \(\dfrac{1}{-x^2+3x-2}=\dfrac{-1}{\left(x-1\right)\left(x-2\right)}=\dfrac{-x-6}{\left(x-1\right)\left(x-2\right)\left(x+6\right)}=\dfrac{\left(-x-6\right)\left(x-3\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)\cdot\left(x+6\right)}\)
\(\dfrac{1}{x^2+5x-6}=\dfrac{1}{\left(x+6\right)\left(x-1\right)}=\dfrac{x-2}{\left(x+6\right)\left(x-1\right)\left(x-2\right)}\)
\(=\dfrac{\left(x-2\right)\left(x-3\right)}{\left(x+6\right)\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
\(\dfrac{1}{-x^2+4x-3}=\dfrac{-1}{\left(x-1\right)\left(x-3\right)}=\dfrac{-\left(x-2\right)\left(x+6\right)}{\left(x-1\right)\left(x-3\right)\left(x+6\right)\left(x-2\right)}\)
