Adding Rational Expressions

Adding Rational Expressions

Adding Rational Expression with Like Denominators

To add when the denominators are the same, add the numerators and keep the same denominator. Then simplify if possible.

Example

$\frac{x}{x+1}+\frac{2}{x+1}+\frac{x+2}{x+1}$ .

To add rational expressions with different denominators:

a. Find the LCM of the denominators. This is the least common

denominator (LCD).

b. For each rational expression, find an equivalent expression with

the LCD. To do so, multiply by 1 using an expression for 1 made up

of factors of the LCD that are missing from the original

denominator.

c. Add the numerators. Write the sum over the LCD.

d. Simplify if possible.