Math Calculators, Lessons and Formulas

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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:

Rational Expressions Example

Solution

1: Factor numerator: Rational Expressions Solution

2: Factor denominator: Rational Expressions Solution

3: Cancel common factors:

Rational Expressions Solution

Example 2

Simplify the following rational expression:

Rational Expressions Example

Solution

1: Factor numerator: Rational Expressions Solution

2: Factor denominator: Rational Expressions Solution

3: Cancel common factors:

Rational Expressions Solution

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)

Rational Expressions 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

Numerator and denominator are quadric trinomials

Factor a quadric trinomial

To factor a quadric trinomial we will use following formula

Factor a quadric trinomial where Factor a quadric trinomial

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:

Factor a quadric trinomial

We then have: Factor a quadric trinomial

Example 4

Simplify the following rational expression:

Rational Expressions Example

Solution

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

1: Factor numerator:

Rational Expressions Solution

2: Factor denominator:

Rational Expressions Solution

3: Cancel common factors:

Rational Expressions Solution

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

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