Question

Answer 1

a: \(\dfrac{x+4y}{x^2-2xy}+\dfrac{x+y}{2y^2-xy}\)

\(=\dfrac{x+4y}{x\left(x-2y\right)}-\dfrac{x+y}{y\left(x-2y\right)}\)

\(=\dfrac{y\left(x+4y\right)-x\left(x+y\right)}{xy\left(x-2y\right)}\)

\(=\dfrac{xy+4y^2-x^2-xy}{xy\left(x-2y\right)}=\dfrac{4y^2-x^2}{xy\left(x-2y\right)}\)

\(=\dfrac{-\left(x-2y\right)\left(x+2y\right)}{xy\cdot\left(x-2y\right)}=\dfrac{-x-2y}{xy}\)

b: \(\dfrac{1}{\left(x-y\right)\left(y-z\right)}+\dfrac{1}{\left(y-z\right)\left(z-x\right)}+\dfrac{1}{\left(z-x\right)\left(x-y\right)}\)

\(=\dfrac{z-x+x-y+y-z}{\left(z-x\right)\left(x-y\right)\left(y-z\right)}=0\)