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

Aug 5, 2016

$x = \frac{7}{2}$

#### Explanation:

$\frac{x - 3}{x - 4} + 4 = 3 \frac{x}{x}$
or
$\frac{x - 3}{x - 4} + 4 = 3$
or
$\frac{x - 3}{x - 4} = - 4 + 3$
or
$\frac{x - 3}{x - 4} = - 1$
or
$x - 3 = - x + 4$
or
$x + x = 4 + 3$
or
$2 x = 7$
or
$x = \frac{7}{2}$

Aug 5, 2016

$x = \frac{7}{2}$

Reworked to make it simpler

#### Explanation:

Note that $\frac{3 x}{x} = 3$ giving

$\frac{x - 3}{x - 4} + 4 = 3$

$\implies \frac{x - 3}{x - 4} + 1 = 0$

But 1 can be written as: $\frac{x - 4}{x - 4}$

$\frac{x - 3}{x - 4} + \frac{x - 4}{x - 4} = 0$

Multiply through out by $\left(x - 4\right)$

$\left(x - 3\right) + \left(x - 4\right) = 0$

$2 x - 7 = 0$

$x = \frac{7}{2}$