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« Multiplying and Dividing Rational Expressions
Rational Expressions: (lesson 3 of 3)

Adding and Subtracting Rational Expressions

Rational Expressions with the Same Denominator

To add/subtract rational expressions with the same denominator

1. Add/subtract the numerators. Write this sum/difference as the numerator over the common denominator.

2. Reduce to lowest terms.

Example 1

Simplify the following:

Adding and Subtracting Example

Solution

These fractions already have a common denominator

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

Adding and Subtracting Solution

2: Reduce to lowest terms:

Adding and Subtracting Solution


Example 2

Simplify the following:

Adding and Subtracting Example

Solution

Again, these already have a common denominator

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

Adding and Subtracting Solution

2: Reduce to lowest terms:

Adding and Subtracting Solution


Exercise 1: Simplify the following expression

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4

Adding or Subtracting Rational Expressions with Different Denominators

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/subtract the numerators.

Example 3:

Simplify the following:

Adding and Subtracting Example

Solution 3:

1: Factor each denominator completely.

Adding and Subtracting Solution

2: Build the LCD of the denominators.

Adding and Subtracting Solution

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

Adding and Subtracting Solution

4: Add the numerators.

Adding and Subtracting Solution


Example 4:

Simplify the following:

Adding and Subtracting Example

Solution 4:

1: Factor each denominator completely.

Adding and Subtracting Solution

2: Build the LCD of the denominators.

Adding and Subtracting Solution

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

Adding and Subtracting Solution

4: Subtract the numerators.

Adding and Subtracting Solution

Exercise 2: Simplify the following expression

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4