# How do you solve the rational equation 1/2 - 3/(2x) = 4/x - 5/12?

Mar 18, 2016

x=6

#### Explanation:

$\frac{1}{2} - \frac{3}{2 x} = \frac{4}{x} - \frac{5}{12}$
arranging the like terms with each other
$\frac{1}{2} + \frac{5}{12} = \frac{4}{x} + \frac{3}{2 x}$
taking L.C.M,
$\frac{6 + 5}{12} = \frac{8 + 3}{2 x}$
$\frac{11}{12} = \frac{11}{2 x}$
simplifying,
$\frac{1}{12} = \frac{1}{2 x}$
$12 = 2 x$
$x = \frac{12}{2}$
$x = 6$