# How do you solve \frac { 18} { x - 2} - \frac { 4} { x - 1} = \frac { 4} { x ^ { 2} - 3x + 2}?

Nov 16, 2017

It has no solution.

#### Explanation:

First of all we do the gcf between $\left(x - 2\right)$ and $\left(x - 1\right)$, that's found by multiplying them with each other,
$\left(x - 2\right) \left(x - 1\right) = {x}^{2} - 3 x + 2$

so now we have this:
$\frac{18 - 4}{{x}^{2} - 3 x + 2} = \frac{4}{{x}^{2} - 3 x + 2}$

we can simplify the divisors:
$\frac{18 - 4}{\cancel{{x}^{2} - 3 x + 2}} = \frac{4}{\cancel{{x}^{2} - 3 x + 2}}$

$18 - 4 = 4$

As you can see, there's no x in the equation, what means that there's no solution to this equation.