a: \(\dfrac{x-1}{x+1}=\dfrac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}\)
\(\dfrac{x+1}{x-1}=\dfrac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}\)
\(\dfrac{1}{x^2-1}=\dfrac{1}{\left(x+1\right)\left(x-1\right)}\)
b: \(\dfrac{x}{x^3-xy^2}=\dfrac{1}{\left(x-y\right)\left(x+y\right)}=\dfrac{x+y}{\left(x-y\right)\left(x+y\right)^2}\)
\(\dfrac{1}{\left(x+y\right)^2}=\dfrac{x-y}{\left(x+y\right)^2\cdot\left(x-y\right)}\)
c: \(\dfrac{5x^2}{x^2+5x+6}=\dfrac{5x^2}{\left(x+2\right)\left(x+3\right)}=\dfrac{5x^2\left(x+5\right)}{\left(x+2\right)\left(x+3\right)\left(x+5\right)}\)
\(\dfrac{2x+3}{x^2+7x+10}=\dfrac{2x+3}{\left(x+2\right)\left(x+5\right)}=\dfrac{\left(2x+3\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)\left(x+5\right)}\)
\(-5=\dfrac{-5\left(x+2\right)\left(x+3\right)\left(x+5\right)}{\left(x+2\right)\left(x+3\right)\left(x+5\right)}\)
