Rational Expressions: (lesson 1 of 3)

## Simplifying Rational Expressions

To simplify a rational expression:

1. Factor numerator as much as possible.

2. Factor denominator as much as possible

3. Cancel common factors.

### Numerator and denominator are linear functions

Example 1

Simplify the following rational expression:

Solution

**1**: Factor numerator:

**2**: Factor denominator:

**3**: Cancel common factors:

Example 2

Simplify the following rational expression:

Solution

**1**: Factor numerator:

**2**: Factor denominator:

**3**: Cancel common factors:

The factors 2 - x and x - 2 are almost the same, but not quite, so they can't be cancelled. Remember to switch the sign out front:
2 - x = -(x - 2)

Exercise 1: Simplify the following expression

### Numerator and denominator are quadric trinomials

Factor a quadric trinomial

**To factor a quadric trinomial we will use following formula **

**where **

Example 3 (IMPORTANT)

Factor the trinomial 2x^{2} + 3x - 2

Solution 3

In this example a = 2, b = 3, c = -2. Plugging these numbers into the quadratic formula we get:

We then have:

Example 4

Simplify the following rational expression:

Solution

Again, the first thing that we will do here is factor the numerator and denominator.

**1**: Factor numerator:

**2**: Factor denominator:

**3**: Cancel common factors:

Nothing else will cancel and so we have reduced this expression to lowest terms.

Exercise 2: Simplify the following expression