« Multiplying and Dividing Rational Expressions

Rational Expressions with the Same Denominator

Example 1

Simplify the following:

Solution

These fractions already have a common denominator

1: Write this sum as the numerator over the common denominator:

2: Reduce to lowest terms:

Example 2

Simplify the following:

Solution

Again, these already have a common denominator

1: Write this sum as the numerator over the common denominator:

2: Reduce to lowest terms:

Exercise 1: Simplify the following expression

Adding or Subtracting Rational Expressions with Different Denominators

Example 3:

Simplify the following:

Solution 3:

1: Factor each denominator completely.

2: Build the LCD of the denominators.

3: Rewrite each rational expression with the LCD as the denominator.

4: Add the numerators.

Example 4:

Simplify the following:

Solution 4:

1: Factor each denominator completely.

2: Build the LCD of the denominators.

3: Rewrite each rational expression with the LCD as the denominator.

4: Subtract the numerators.

Exercise 2: Simplify the following expression