Example

Solve for $w$: $\quad \displaystyle \frac{1}{w-4}+\frac{3}{w+2} = \frac{10}{w^2-2w-8}$

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 $(w-4)(w+2)$. Multiplying both sides of the equation by $(w-4)(w+2)$ will clear fractions.

Our possible solution is not a restricted value. The equation has the single solution $w=5$.