# How do you solve 3/(2x-9)-2=(5x)/(2x-9) and check for extraneous solutions?

Sep 9, 2016

$x = \frac{7}{3}$

#### Explanation:

First you have to find the least common denominator $L C D$ that is:

$2 x - 9$

Now, a denominator cannot be zero, then:

$2 x - 9 \ne 0 \implies x \ne \frac{9}{2}$

$\therefore x = \frac{9}{2} \notin F E$ (Field of existence of the equation), and it cannot be a solution.

Now, you simplyfy the equation using the $L C D$

$\frac{3 - 2 \left(2 x - 9\right)}{\cancel{\left(2 x - 9\right)}} = \frac{5 x}{\cancel{\left(2 x - 9\right)}}$

$\implies 3 - 4 x + 18 = 5 x$

Now move all the x therms in the LHS and the other in the RHS

$- 4 x - 5 x = - 21$
$- 9 x = - 21$
$9 x = 21$
$x = {\cancel{21}}^{7} / {\cancel{9}}^{3} = \frac{7}{3}$

with $x \in F E$