How do you solve (y+2)/y=1/(y-5)?

Dec 21, 2015

$y = 2 + \sqrt{14}$

Explanation:

First multiply out to get rid of denominators:
$\left(y + 2\right) \left(y - 5\right) = 1 \cdot y$
${y}^{2} - 3 y - 10 - y = 0$
${y}^{2} - 4 y - 10 = 0$
Using completing the squares
${\left(y - 2\right)}^{2} - 10 - 4 = 0$
${\left(y - 2\right)}^{2} = 14$
$y = 2 + \sqrt{14}$