Wiskunde Multiple Choice Vraag

Wat is de oplossingen- verzameling van de rationale vergelijking $\frac{3}{x-1}+\frac{5x}{x+1}=\frac{3x+3}{x^2-1}$	A. { −1 }
	B. { 0 }
	C. { 0, 1 }
	D. { }
	E. geen van de vorige

[ 5-6389 - op net sinds 23.2.2026-(E)- ]

Translation in E N G L I S H

What is the solution set of the rational equation $\frac{3}{x-1}+\frac{5x}{x+1}=\frac{3x+3}{x^2-1}$	A. { −1 }
	B. { 0 }
	C. { 0, 1 }
	D. { }
	E. none of these

Oplossing - Solution

$\inline\\\frac{3}{x-1}+\frac{5x}{x+1}=\frac{3x+3}{x^2-1}\Leftrightarrow\frac{3x+3+5x^2-5x}{x^2-1}=\frac{3x+3}{x^2-1}\Leftrightarrow\frac{5x^2-2x+3}{x^2-1}=\frac{3x+3}{x^2-1}\\\Leftrightarrow 5x^2-2x+3=3x+3\quad\wedge\quad x^2\neq 1\\\Leftrightarrow 5x^2-5x=0\quad\wedge\quad x^2\neq 1\\\Leftrightarrow x(x-1)=0\quad\wedge\quad x^2\neq 1\\\Leftrightarrow\left(x=0\;\vee x=1\right)\quad\wedge\quad x^2\neq 1\\\Leftrightarrow x=0$