2. Rational equations are equations that involve fractions
Rational equations are equations that involve fractions. The ones we mostly care about in algebra are equations where the fraction has a variable.

3. You’ve already solved proportions, which are one kind of rational equation. Now we’re going to solve others.

5. A way that always works to solve rational equations is to multiply every term by something that will cancel out all the fractions.

7. Now solve 28 + x = 12x = 11x /11 = x

8. Technically what you should multiply by is the least common denominator. However, you can actually multiply by any common denominator. (It doesn’t have to be the least.)

9. Hint for the future: You should always check to be sure the answer(s) you get doesn’t leave the original equation undefined.  In Algebra I it won’t, but it might later on.

16. Often when you multiply, the result will be a quadratic equation.

19. Now solve. 8x = x + 3 + x2 + 3x. 0 = x + 3 + x2 + 3x – 8x
Now solve 8x = x x2 + 3x 0 = x x2 + 3x – 8x 0 = x2 – 4x = (x – 3)(x – 1) So … x = 3 or 1

20. Back in the original equation,. _ If x = 3, both sides would be 1
Back in the original equation, _ If x = 3, both sides would be 1.3 If x = 1, both sides would be 2