# Rational Expression

**Textbook sections and practice problems**

6.1: 61–71 odd

6.3: 7-23 odd, 33-39 odd, 43-49 odd

**Division of rational expressions**

assuming B ≠ 0 , C ≠ 0 , and D ≠ 0

**Example 1**

Completely simplify. Verify the simplified formula for x =1.

**Example 2**

Completely simplify. Verify the simplified formula for t = 2 .

**Example 3**

Completely simplify. Verify the simplified formula for t = 2 .

**Complex Fractions**

A complex fraction is any fraction whose numerator or denominator contains another fraction.

**Simplifying complex rational expressions – Strategy A**

1. Simplify (add and/or subtract, as necessary) the expressions in the numerator
and

denominator.

2. Reciprocate the expression in the denominator and multiply with the
expression in the

numerator.

3. Simplify the remaining expression.

**Example 4**

Completely simplify Verify the simplified formula for x = −1.

**Example 5**

Completely simplify . Verify the simplified formula for y = 3 .

**Simplifying complex rational expressions – Strategy B**

1. Determine the LCD of all of the expressions in the fraction regardless of
whether the

expressions occur in the numerator or denominator.

2. Multiply along the main fraction bar by the LCD determined in step 1.
Remember to

distribute the LCD through both the numerator and denominator.

3. Simplify each product.

4. If you correctly applied steps 1 – 3, the expression is no longer a complex
rational

expression; simplify the remaining expression.

**Example 6**

Completely simplify . Verify your formula when x = 2 and y = 1.

**Example 7**

Completely simplify . Verify your formula when x = 1.

**Example 8**

Completely simplify Verify your result using t = 1 and h = 2 .

**Example 9**

Completely simplify Verify your result when y = 2.