Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\left ( x-\frac 1x \right ):\left ( 1+\frac 1x \right )=$	A. 1
	B. − 1
	C. x − 1
	D. − x
	E. x
	F. $\large\boldsymbol{\frac {x^2\,-\:1} {x} }$
	G. $\large\boldsymbol{\frac {x\,-\,1} {x\,+\,1} }$

[ B-1467 - op net sinds 17.4.10-(E)-3.11.2023 ]

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\left ( x-\frac 1x \right )\textbf{:}\left ( 1+\frac 1x \right )=\left ( \frac{x^2}{x}-\frac 1x \right )\textbf{:} \left ( \frac xx+\frac 1x \right )\\=\frac{x^2-1}{x}\textbf{:}\frac{x+1}{x}=\frac{x^2-1}{x}\cdot \frac{x}{x+1}=\frac{(x-1)(x+1)x}{x(x+1)}= \cdots$