Example

Solve for $x$: $\quad \displaystyle 4 + \frac{3}{x-2} = \frac{3}{(x-1)(x-2)}$

Solution

Since this equation does not set a single fraction equal to another single fraction, it cannot be solved by cross multiplying. Instead we clear fractions.

The denominators of the individual fractions are

so the LCM is $(x-1)(x-2)$. Multiplying both sides of the equation by $(x-1)(x-2)$ will clear fractions.

We have two possible solutions, $x=1/4$ or $x=2$, but we must notice that $x=2$ is a restricted value. The equation has the single solution $x=1/4$.