Question

What is the simplified algebraic expression of [{2x+y}/{x+y} - 1]divided by [1- {y/x+y}]

Answer 1

$$\begin{gathered} \frac{{\displaystyle \frac{2\mathrm{x}+\mathrm{y}}{\mathrm{x}+\mathrm{y}}}-1}{1-{\displaystyle \frac{\mathrm{y}}{\mathrm{x}+\mathrm{y}}}}=\frac{{\displaystyle \frac{2\mathrm{x}+\mathrm{y}-\left(\mathrm{x}+\mathrm{y}\right)}{\mathrm{x}+\mathrm{y}}}}{{\displaystyle \frac{\mathrm{x}+\mathrm{y}-\mathrm{y}}{\mathrm{x}+\mathrm{y}}}} \\ =\frac{{\displaystyle \frac{2\mathrm{x}+\mathrm{y}-\mathrm{x}-\mathrm{y}}{\mathrm{x}+\mathrm{y}}}}{{\displaystyle \frac{\mathrm{x}+\mathrm{y}-\mathrm{y}}{\mathrm{x}+\mathrm{y}}}} \\ =\frac{{\displaystyle \frac{\mathrm{x}}{\mathrm{x}+\mathrm{y}}}}{{\displaystyle \frac{\mathrm{x}}{\mathrm{x}+\mathrm{y}}}} \\ =\frac{x}{x+y}\times \frac{x+y}{x} \\ =1 \\ Hence,\frac{{\displaystyle \frac{2x+y}{x+y}-1}}{\mathbf{1}\mathbf{-}{\displaystyle \frac{y}{x+y}}}\mathbf{=}\mathbf{1} \end{gathered}$$