# How do you solve 1/x+2/3=2 and check for extraneous solutions?

$x = \frac{3}{4}$
Multiply through by $3 x$ to get $3 + 2 x = 6 x$ which is linear with the only solution $x = \frac{3}{4}$. Check this back in the original equation: $\frac{4}{3} + \frac{2}{3} = 2$