Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{b}{\frac{a}{b}-1}-\frac{b}{1-\frac{b}{a}}=$	A. − b
	B. b
	C. 2b
	D. ab
	E. − ab

[ B-8685 - op net sinds 4.5.2021-(E)-30.10.2023 ]

Translation in E N G L I S H

see above

Oplossing - Solution

$\frac{b}{\frac{a}{b}-1}-\frac{b}{1-\frac{b}{a}} =\frac{b}{\frac{a-b}{b}}-\frac{b}{\frac{a-b}{a}} =\frac{b^2}{a-b}-\frac{ab}{a-b}=\frac{b^2-a^2}{a-b}=\frac{b(b-a)}{a-b}=-b$