These free video lessons with examples and solutions help Algebra students learn how to simplify algebraic rational expressions.

**Related Pages**

Simplifying Rational Expressions

Adding Rational Expressions

Subtracting Rational Expressions

Multiplying Rational Expressions

Dividing Rational Expressions

Algebraic Expressions

A rational expression is a fraction in which the numerator and/or the denominator are polynomials.

**Examples:**

The following diagram shows how to simplify rational expressions. Scroll down the page for more examples and solutions on simplifying rational expressions.

In this lesson, we will look at simplifying rational expressions. A rational expression has been simplified or reduced to lowest terms if all common factors from the numerator and denominator have been canceled.

- We first need to factor the polynomials
- Cancel any common factors from the top and bottom of the rational expression.

**Example:**

Simplify each of the following rational expressions:

**Solution:**

**Simplifying Rational Expressions - Level 1**

**Example:**

Simplify

(4x^{3} + 8x^{2})/2x

**Simplifying Rational Expressions - Level 2**

**Example:**

Simplify

(7x^{2} + 28x)/(x^{2} + 8x + 16)

**Simplifying Rational Expressions - Level 3**

**Example:**

Simplify

(4x^{2} + 4x + 1)/(2x^{3} + 11x^{2} + 5x)

**How To Write Rational Expressions In Lowest Terms?**

Step 1: Factor them

Step 2: Cancel to write in lowest terms

Give the domain of the expressions

**Examples:**

Simplify

a) (x + 2)/(x^{2} + 5x + 6)

b) (x^{2} + 2x - 15)/(x^{2} + x - 12)

**Rational Expressions: Writing In Lowest Terms**

How to reduce a rational expression involving a cubic polynomial and a quadratic polynomial?

**Example:**

Simplify

(x^{3} + 1)/(x^{2} + 7x + 6)

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