Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Wat is het resultaat van de volgende deling? $https://latex.codecogs.com/png.image?\dpi{110}\frac{1+\frac 1a}{a}:\frac{a}{1-\frac 1a}$	A. − 1
	B. a² − 1
	C. $\large\boldsymbol{-\,\frac {1} {a^2} }$
	D. $\large\boldsymbol{\frac {a\,+\,1} {a\,-\,1} }$
	E. $\large\boldsymbol{\frac {a^2-1} {a^4} }$

[ B-5003 - op net sinds 15.11.16-(E)-22.10.2026 ]

Translation in E N G L I S H

What is the result of the following division ? $https://latex.codecogs.com/png.image?\dpi{110}\frac{1+\frac 1a}{a}:\frac{a}{1-\frac 1a}$	A. − 1
	B. a² − 1
	C. $\boldsymbol{-\,\frac {1} {a^2} }$
	D. $\boldsymbol{\frac {a\,+\,1} {a\,-\,1} }$
	E. $\boldsymbol{\frac {a^2-1} {a^4} }$

Oplossing - Solution

$\large\frac{1+\frac 1a}{a}\;\textbf{:}\;\frac{a}{1-\frac 1a}=\frac{\frac{a+1}{a}}{a}\;\textbf{:}\;\frac{a}{\frac{a-1}a}=\frac{\frac{a+1}{a}}{a}\cdot \frac{\frac{a-1}{a}}{a}=\frac{a+1}{a^2}\cdot \frac{a-1}{a^2}=\frac{a^2-1}{a^4}$