How do you solve 1+x/(2-x)=(6x)/(2-x) and check for extraneous solutions?

Apr 10, 2018

$x = \frac{1}{3}$

Explanation:

Multiply everything by $\left(2 - x\right)$ to get rid of the fractions

$1 \left(2 - x\right) + x = 6 x$

$\implies$ $2 - x + x = 6 x$

$\implies$ $2 = 6 x$

$x = \frac{2}{6}$

$x = \frac{1}{3}$