Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\frac{\frac{1}{a}+\frac{1}{b}}{\frac{1}{a^2}-\frac{1}{b^2}}=$	A. a − b
	B. $\frac{1}{a-b}$
	C. $\frac{ab}{a-b}$
	D. $\frac{ab}{b-a}$
	E. $\frac{b-a}{ab}$

[ 3,4-0771 - op net sinds 17.10.2025-(E)- ]

Translation in E N G L I S H

See above

Oplossing - Solution

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

$\frac{\frac{1}{a}+\frac{1}{b}}{\frac{1}{a^2}-\frac{1}{b^2}}=$	A. a − b
	B. \(\frac{1}{a-b}\)
	C. \(\frac{ab}{a-b}\)
	D. \(\frac{ab}{b-a}\)
	E. \(\frac{b-a}{ab}\)