# How do you solve  5/x + 6/x = 12?

Apr 17, 2016

## $x = \frac{11}{12}$

#### Explanation:

Make sure that every term in the equation (including the total) has a common denominator.

12 as a fraction is $\frac{12}{1}$

So what we have is:
$\frac{5}{x} + \frac{6}{x} = \frac{12}{1}$

We need to find the LCD (least common denominator), which in this case would be $x$. Both $\frac{5}{x}$ and $\frac{6}{x}$ have the common denominator of $x$ but $\frac{12}{1}$ doesn't. To make sure that it does have the common denominator of $x$, we need to multiply both the denominator and the numerator by $x$ ($\frac{12 \times x}{1 \times x} = \frac{12 x}{x}$).

Now we have:
$\frac{5}{x} + \frac{6}{x} = \frac{12 x}{x}$

Since all of the terms have a common denominator, we can just simply evaluate for what $x$ is equal to.
$5 + 6 = 12 x$
$11 = 12 x$
$\frac{11}{12} = x$