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

Jun 15, 2018

$x = \frac{9}{4} + \frac{i}{4} \cdot \sqrt{3}$ or $x = \frac{9}{4} - \frac{\sqrt{3}}{4} \cdot i$

#### Explanation:

Multiplying by $\left(x - 3\right) \left(x - 4\right)$ we get

$\left(4 x - 3\right) \left(x - 3\right) + \left(x - 3\right) \left(x - 4\right) = x \left(x - 4\right)$
and this is

$4 {x}^{2} - 18 x + 21 = 0$
so we have
${x}^{2} - \frac{9}{2} x + \frac{21}{4} = 0$
${x}_{1 , 2} = \frac{9}{4} \pm i \frac{\sqrt{3}}{4}$