# How do you solve x+ \frac { 6 } { x } = 5?

Oct 12, 2016

$x = 2$ and $x = 3$

#### Explanation:

I would approach this problem by finding the common denominator on both sides of the equation then simplify the equation.

$x + \frac{6}{x} = 5$

The common denominator (LCD) is $x$

$\frac{{x}^{2} + 6}{1 \cancel{x}} = \frac{5 x}{1 \cancel{x}}$

Simplify the $x$'s or use another method but you will see that you will end up simplifying the $x$

${x}^{2} + 6 = 5 x$

${x}^{2} - 5 x + 6 = 0$

Here, too you can use any method you are comfortable with, as for me I always find the $\Delta$

$\Delta = {b}^{2} - 4 a c$, with $a = 1$, $b = - 5$ and $c = 6$

$\Delta = {\left(- 5\right)}^{2} - 4 \left(1\right) \left(6\right) = 1 \implies \sqrt{\Delta} = \pm 1$

${x}_{1} = \frac{- b + \sqrt{\Delta}}{2 a}$ and ${x}_{2} = \frac{- b - \sqrt{\Delta}}{2 a}$

${x}_{1} = \frac{5 + 1}{2} = 3$ and ${x}_{2} = \frac{5 - 1}{2} = 2$

So, $x = 2$ and $x = 3$ is your solution.