Concept preview

What you will be able to do

1. 01Solve rational equations by multiplying through by the LCD to clear fractions
2. 02Check solutions against the restrictions and reject extraneous roots
3. 03Apply rational equations to rate, work, and reciprocal problems

An equation with fractions is annoying; an equation without them is easy. So the whole strategy for a rational equation is to get rid of the fractions in one stroke by multiplying every term by the LCD (lowest common denominator). Just as $\dfrac{x}{3} + \dfrac{x}{4} = 7$ becomes $4x + 3x = 84$ after multiplying by 12, the denominators vanish and you are left with an ordinary equation to solve.