A rational expression is a fraction in which the numerator and/or the denominator are polynomials.

Example:

3x-5

4x^2+3x

Just like with simple fractions, in order to add or subtract rational expressions one must find a common denominator.

Common denominator: a shared multiple of the denominators of two or more fractions.

One way to do this is multiplying each fraction by the denominator of the other fraction.

Changing one denominator (fully written out):

3x+4 + 2x-1 = (3x+4) * 2 = 6x+8

x+2 2x+4 (x+2) * 2 2x+4

6x+8 + 2x-1 = (6x+8)+(2x-1) = 8x+7

2x+4 2x+4 2x+4 2x+4

Changing two denominators:

2x+3 + 4x-7 = 6x+9 + 8x-14 = 14x-5

2x+2 3x+3 6x+6 6x+6 6x+6