Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{1}{2+\sqrt 3}+\frac{2}{\sqrt 3 - 1}$ is gelijk aan	A.
	B. 2
	C. 3
	D. 4
	E.

[ 4-2059 - op net sinds 30.3.2020-(E)-4.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\frac{1}{2+\sqrt 3}+\frac{2}{\sqrt 3 - 1}$ is equal to	A.
	B. 2
	C. 3
	D. 4
	E.

Oplossing - Solution

$\\\frac{1}{2+\sqrt 3}+\frac{2}{\sqrt 3-1}=\frac{2-\sqrt3}{(2+\sqrt3)(2-\sqrt3)}+\frac{2.(\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)}\\=\frac{2-\sqrt3}{4-3}+\frac{2.(\sqrt3+1)}{3-1}=2-\sqrt3+\sqrt3+1=3$