# Algebra 2 Rational Expressions Homework Help

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:

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

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:

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

## Random Quote

Do not worry about your difficulties in mathematics, I assure you that mine are greater.

Albert Einstein

## Random Quote

Go down deep enough into anything and you will find mathematics.

Dean Schlicter

Rational Expressions: (lesson 2 of 3)

## Multiplying and Dividing Rational Expressions

### Multiplication

To Multiply a rational expression:

1. Factor all numerators and denominators.

2. Cancel all common factors.

3. Either multiply the denominators and numerators together or leave the solution in factored form.

Example 1

Multiply and then simplify the product

Solution

Example 2

Multiply the following rational expressions:

Solution

**1**: Factor all numerators and denominators:

**2**: Cancel all common factors:

**3**: Multiply the denominators and numerators:

### Division of rational expressions

**When we divide rational functions we multiply by the reciprocal.**

Example 3:

Perform the indicated operations:

Solution 3:

Example 4:

Perform the indicated operations:

Solution 4:

## Random Quote

The infinite! No other question has ever moved so profoundly the spirit of man.

David Hilbert

## Random Quote

Do not worry about your difficulties in mathematics, I assure you that mine are greater.

Albert Einstein