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

Jan 10, 2016

$y = 2 \pm \sqrt{14}$

Explanation:

Multiply through by the denominators to remove the fractions.

$\left(y + 2\right) \left(y - 5\right) = y$

Expand and solve.

${y}^{2} - 3 y - 10 = y$
${y}^{2} - 4 y - 10 = 0$
${\left(y - 2\right)}^{2} - 14 = 0$
$y = 2 \pm \sqrt{14}$