Multiplying and Dividing Rational Expressions »

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 2x² + 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’ll 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