Question

State true or false:

If $\frac{1}{x+1}+\frac{1}{x-2}=\frac{1}{x-3}$, then $x$ is $5$ or $0$.

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{1}{x+1}+\frac{1}{x-2}=\frac{1}{x-3}$

$\frac{x-2+x-1}{(x+1)(x-2)}=\frac{1}{x-3}$
$(2x-1)(x-3)=(x-2)(x+1)$
$2x^2-6x-x+3=x^2-2x+x-2$
$x^2-6x+5=0$
$x^2-5x-x+5=0$
$(x-5)(x-1)=0$
$x=1,5$