# How do you solve 12/x+3/4=3/2?

Feb 23, 2016

$x = 16$

#### Explanation:

Generally when solving a problem like this one I choose to multiply all terms by a common denominator. In this case the common denominator is $4 x$.
$\left(4 x\right) \left(\frac{12}{x} + \frac{3}{4} = \frac{3}{2}\right)$

$48 + 3 x = 6 x$

$48 = 3 x$

$16 = x$

There is another approach to solving this problem, and that is to subtract $\frac{3}{4}$ from each side of the equation first.
$\frac{12}{x} + \frac{3}{4} - \frac{3}{4} = \frac{3}{2} - \frac{3}{4}$

$\frac{12}{x} = \frac{6}{4} - \frac{3}{4}$

$\frac{12}{x} = \frac{3}{4}$

Now this is a simple ratio which can be solved by cross multiplying.

$48 = 3 x$

$16 = x$