Question

  

Answer 1

a) \(\dfrac{x+y}{x+2y}:\dfrac{x+3y}{x+2y}:\dfrac{x+y}{x+3y}\)

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

\(=\dfrac{x+y}{x+2y}:\dfrac{x+y}{x+2y}\)

\(=1\)

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

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

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

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