And what exactly was your problem anyway?

You have transformed an equation with fractions into one with no fractions. That was the whole purpose of multiplying each side with LCM.

So you should now continue solving the equation normally and get the appropriate result.... (as Deveno did)

BUT BY ALL MEANS you should never forget that the original equation is not equivalent(in most times) with the values you get for the variable in the final step, because it may make one of the denominators zero.

In other words the solution you get is a possible one but not a sure one. So you should verify that the final answer verifies the original equation.

Example:

How you would solve the following one?

$\displaystyle \frac{{{x^2} - 2x}}{{x - 3}} = \frac{1}{4} + \frac{{8x - 18}}{{2(x - 3)}}$