Wiskunde Multiple Choice Vraag

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

[ B-6142 - op net sinds 25.10.2024-(E)- ]

Translation in E N G L I S H

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

Oplossing - Solution

1^ste manier :
$\frac{a+\frac{a}{b}}{a-\frac{a}{b}}=\frac{\frac{ab}{b}+\frac{a}{b}}{\frac{ab}{b}-\frac{a}{b}}=\frac{\frac{ab+a}{b}}{\frac{ab-a}{b}}=\frac{ab+a}{b}\cdot\frac{b}{ab-a}=\frac{a(1+b)}{a(b-1)}=\frac{b+1}{b-1}$
2^de manier :
$\frac{a+\frac{a}{b}}{a-\frac{a}{b}}=\frac{1+\frac1b}{1-\frac1b}=\frac{\frac{b+1}{b}}{\frac{b-1}{b}}=\frac{b+1}{b}\cdot\frac{b}{b-1}=\frac{b+1}{b-1}$