# How do you solve  (x-1)/x + 7/(3x) = 9/(4x) ?

Oct 2, 2015

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

#### Explanation:

Multiply both sides by $12 x$, (the LCM of x, 3x and 4x)

$12 \left(x - 1\right) + 7 \cdot 4 = 9 \cdot 3$
$12 x - 12 + 28 = 27$

Isolate the x

$12 x - 12 = 27 - 28$
$12 x - 12 = - 1$
$12 x = - 1 + 12$
$x = \frac{11}{12}$

Check if the answer doesn't cause an absurd, in this case,
$x \ne 0$
$3 x \ne 0 \rightarrow x \ne 0$
$4 x \ne 0 \rightarrow x \ne 0$