Example

Solve for $w$: $\qquad \displaystyle \frac{w}{w-4} = \frac{4}{w-4}-\frac{4}{5}$

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 least common multiple (LCM) of the denominators is $5(w-4)$. Multiplying both sides of the equation by $5(w-4)$ will clear fractions.

It looks like the solution is $w=4$, but this is a restricted value! The only possible solution is not a solution at all! The equation has no solution.