Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\frac{a^{-1}+b}{a+b^{-1}}$ is gelijk aan	A. $\boldsymbol{1}$
	B. $\large\boldsymbol{\frac ab }$
	C. $\large\boldsymbol{\frac ba }$
	D. $\large\boldsymbol{\frac {(1\,+\,ab)^2} {ab} }$
	E. $\large\boldsymbol{\frac {b(1\,+\,b)} {a(1\,+\,a)} }$

[ B-2953 - op net sinds 14.8.12-(E)-25.7.2024 ]

Translation in E N G L I S H

$\frac{a^{-1}+b}{a+b^{-1}}$ is equal to See above

Oplossing - Solution

${\color{DarkGreen} \frac{a^{-1}+b}{a+b^{-1}}=\frac{\frac{1}{a}+b}{a+\frac{1}{b}}=\frac{\frac{1+ab}{a}}{\frac{ab+1}{b}}=\frac{1+ab}{a}\cdot \frac{b}{ab+1}=\cdots }$

$\frac{a^{-1}+b}{a+b^{-1}}$ is gelijk aan	A. \(\boldsymbol{1}\)
	B. \(\large\boldsymbol{\frac ab }\)
	C. \(\large\boldsymbol{\frac ba }\)
	D. \(\large\boldsymbol{\frac {(1\,+\,ab)^2} {ab} }\)
	E. \(\large\boldsymbol{\frac {b(1\,+\,b)} {a(1\,+\,a)} }\)