a: \(\dfrac{x-y}{2x^2-4xy+2y^2}=\dfrac{x-y}{2\left(x-y\right)^2}=\dfrac{1}{2\left(x-y\right)}=\dfrac{x+y}{2\left(x-y\right)\left(x+y\right)}\)
\(\dfrac{x+y}{2x^2+4xy+2y^2}=\dfrac{x+y}{2\left(x+y\right)^2}=\dfrac{1}{2\left(x+y\right)}=\dfrac{x-y}{2\left(x-y\right)\left(x+y\right)}\)
\(\dfrac{1}{y^2-x^2}=\dfrac{-1}{\left(x-y\right)\left(x+y\right)}=\dfrac{-2}{2\left(x-y\right)\left(x+y\right)}\)
b: \(\dfrac{1}{x^2+8x+15}=\dfrac{1}{\left(x+3\right)\left(x+5\right)}=\dfrac{x+3}{\left(x+3\right)^2\cdot\left(x+5\right)}\)
\(\dfrac{1}{x^2+6x+9}=\dfrac{1}{\left(x+3\right)^2}=\dfrac{x+5}{\left(x+5\right)\left(x+3\right)^2}\)
c: \(\dfrac{1}{\left(a-b\right)\left(b-c\right)}=\dfrac{a-c}{\left(a-b\right)\left(b-c\right)\left(a-c\right)}\)
\(\dfrac{1}{\left(c-b\right)\left(c-a\right)}=\dfrac{1}{\left(a-c\right)\left(b-c\right)}=\dfrac{a-b}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}\)
\(\dfrac{1}{\left(b-a\right)\left(a-c\right)}=\dfrac{-1}{\left(a-b\right)\left(a-c\right)}=\dfrac{-b+c}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}\)
