# How do you solve \frac{2x}{x+4}=\frac{5}{x}?

Mar 20, 2018

Cross multiplication and then a quadratic equation

#### Explanation:

Firstly, cross multiply the two denominators in order to remove the division signs,

$\frac{2 x}{x + 4} = \frac{5}{x}$

$2 x \cdot x = 5 \cdot \left(x + 4\right)$

$2 {x}^{2} = 5 x + 20$

Put all terms on one side (easier to keep ${x}^{2}$ positive)

$2 {x}^{2} - 5 x - 20 = 0$

Divide through by any common factors (If there are any, there aren't in this case.)

Now either use the quadratic formula or try to factorise it yourself. In this example factorisation using integers is impossible so just use the formula.

You should end up with an answer of $x = \frac{5 \pm \sqrt{185}}{4}$