Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

${\color{DarkBlue} \frac{x\cdot y}{x^{-1}-y^{-1}}\;\: \; \; is\; \; gelijk\;\; aan } \newline {\color{DarkBlue} \textbf{A.}\: \frac{x^2\cdot y^2}{y-x}\; \; \; \textbf{B.}\: \frac{x^2\cdot y^2}{x-y}\; \; \; \textbf{C.}\: \frac{1}{y-x}\; \; \; \textbf{D.}\: y-x\; \; \; \textbf{E.}\;\: x\cdot y\left ( x-y \right ) }$

[ B-3380 - op net sinds 14.8.12-(E)-2.11.2023 ]

Translation in E N G L I S H

${\color{DarkBlue} \frac{x\cdot y}{x^{-1}-y^{-1}}\;\: \; \; is\;\; equal\;\; to } \newline {\color{DarkBlue} \textbf{A.}\: \frac{x^2\cdot y^2}{y-x}\; \; \; \textbf{B.}\: \frac{x^2\cdot y^2}{x-y}\; \; \; \textbf{C.}\: \frac{1}{y-x}\; \; \; \textbf{D.}\: y-x\; \; \; \textbf{E.}\;\: x\cdot y\left ( x-y \right ) }$

Oplossing - Solution

${\color{DarkGreen} \frac{x\cdot y}{x^{-1}-y^{-1}}= \frac{x\cdot y}{\frac{1}{x}-\frac{1}{y}}= \frac{x\cdot y}{\frac{y-x}{x\cdot y}}=x\cdot y\cdot \frac{x\cdot y}{y-x}=\frac{x^2\cdot y^2}{y-x} }$