Question

State true or false:

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

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{x}{x-1}+\frac{x-1}{x}=2\frac{1}{2}$
$x^2+(x-1{)}^2=\frac{5}{2}x(x-1)$
$2(x^2+x^2-2x+1)=5x^2-5x$
$4x^2-4x+2=5x^2-5x$
$x^2-x-2=0$
$x^2-2x+x-2=0$
$(x-2)(x+1)=0$
$x=-1,2$