# How do you solve 1/x + 1 = x/2?

May 21, 2018

${x}_{1} = 1 + i$ or ${x}_{2} = 1 - i$

#### Explanation:

It must be $x$ not equal to zero, then we multiply by $x$
getting
$1 + x = {x}^{2} / 2$
multipling by $2$ and rearranging we have
$0 = {x}^{2} - 2 x + 2$
using the quadratic formula we get
${x}_{1 , 2} = 1 \setminus \pm \sqrt{- 1}$ so
${x}_{1} = 1 + i$
${x}_{2} = 1 - i$