Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\frac {\sqrt 5+3} {\sqrt 5-3}$ is gelijk aan	A. $-\,3,5+2\sqrt{15}$
	B. $-\,3,5-3\sqrt5$
	C. $-\,3,5+1,5\sqrt5$
	D. $-\,3,5-1,5\sqrt5$
	E. $-\,3,5+1,5\sqrt{15}$

[ 4-0774 - op net sinds 27.3.13-(E)-27.12.2024 ]

Translation in E N G L I S H

$\frac {\sqrt 5+3} {\sqrt 5-3}$ is equal to	A. $-\,3,5+2\sqrt{15}$
	B. $-\,3,5-3\sqrt5$
	C. $-\,3,5+1,5\sqrt5$
	D. $-\,3,5-1,5\sqrt5$
	E. $-\,3,5+1,5\sqrt{15}$

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\\frac{\sqrt5+3}{\sqrt5-3}\!=\!\frac{(\sqrt5+3)^2}{(\sqrt5\!-\!3)(\sqrt5+3)}\!=\!\frac{5\!+\!6\sqrt5\!+\!9}{5-9}\!=\!\frac{14+6\sqrt5}{-4}\!=\!\frac{7\!+\!3\sqrt5}{-2}\!=\!-\frac72-\frac 32\sqrt5$

$\frac {\sqrt 5+3} {\sqrt 5-3}$ is gelijk aan	A. \(-\,3,5+2\sqrt{15}\)
	B. \(-\,3,5-3\sqrt5\)
	C. \(-\,3,5+1,5\sqrt5\)
	D. \(-\,3,5-1,5\sqrt5\)
	E. \(-\,3,5+1,5\sqrt{15}\)

$\frac {\sqrt 5+3} {\sqrt 5-3}$ is equal to	A. \(-\,3,5+2\sqrt{15}\)
	B. \(-\,3,5-3\sqrt5\)
	C. \(-\,3,5+1,5\sqrt5\)
	D. \(-\,3,5-1,5\sqrt5\)
	E. \(-\,3,5+1,5\sqrt{15}\)