How do you solve 9/2x+2=8/x?

Jan 10, 2016

Answer:

$x = \frac{- 2 \pm 2 \sqrt{37}}{9}$

Explanation:

Multiply through by 2x to remove the fractions.

$9 {x}^{2} + 4 x = 16$
$9 {x}^{2} + 4 x - 16 = 0$
$x = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \cdot 9 \cdot - 16}}{18}$
$x = \frac{- 4 \pm \sqrt{592}}{18}$
$x = \frac{- 4 \pm 4 \sqrt{37}}{18}$
$x = \frac{- 2 \pm 2 \sqrt{37}}{9}$