Question

Answer 1

a: \(=\dfrac{x\left(x-y\right)}{y}\cdot\dfrac{y\left(x+y\right)}{x\left(x-y\right)}\cdot\dfrac{x^2+2}{x^2-1}=\dfrac{\left(x+y\right)\left(x^2+2\right)}{x^2-1}\)

b: \(=\dfrac{x^2+1}{3x}\cdot\dfrac{x-1}{x^2+1}\cdot\dfrac{x\left(x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+x+1}{\left(x+1\right)^2}\)

\(=\dfrac{x-1}{3x}\cdot\dfrac{x}{x-1}\cdot\dfrac{1}{\left(x+1\right)^2}\)

\(=\dfrac{1}{3\left(x+1\right)^2}\)

c: \(=\dfrac{x^2+y}{y}:\left(\dfrac{z}{x^2}\cdot\dfrac{x^2+y}{xy}\right)\)

\(=\dfrac{x^2+y}{y}\cdot\dfrac{x^3y}{\left(x^2+y\right)z}=\dfrac{x^3}{z}\)