Algebra Tutorials! Tuesday 19th of October Home Scientific Notation Notation and Symbols Linear Equations and Inequalities in One Variable Graphing Equations in Three Variables What the Standard Form of a Quadratic can tell you about the graph Simplifying Radical Expressions Containing One Term Adding and Subtracting Fractions Multiplying Radical Expressions Adding and Subtracting Fractions Multiplying and Dividing With Square Roots Graphing Linear Inequalities Absolute Value Function Real Numbers and the Real Line Monomial Factors Raising an Exponential Expression to a Power Rational Exponents Multiplying Two Fractions Whose Numerators Are Both 1 Multiplying Rational Expressions Building Up the Denominator Adding and Subtracting Decimals Solving Quadratic Equations Scientific Notation Like Radical Terms Graphing Parabolas Subtracting Reverses Solving Linear Equations Dividing Rational Expressions Complex Numbers Solving Linear Inequalities Working with Fractions Graphing Linear Equations Simplifying Expressions That Contain Negative Exponents Rationalizing the Denominator Decimals Estimating Sums and Differences of Mixed Numbers Algebraic Fractions Simplifying Rational Expressions Linear Equations Dividing Complex Numbers Simplifying Square Roots That Contain Variables Simplifying Radicals Involving Variables Compound Inequalities Factoring Special Quadratic Polynomials Simplifying Complex Fractions Rules for Exponents Finding Logarithms Multiplying Polynomials Using Coordinates to Find Slope Variables and Expressions Dividing Radicals Using Proportions and Cross Solving Equations with Radicals and Exponents Natural Logs The Addition Method Equations
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# Simplifying Rational Expressions

After studying this lesson, you will be able to:

• Simplify rational expressions.

A rational expression is a fraction that contains at least one variable.

There are basically 2 steps to simplify a rational expression :

1. Factor the numerator and the denominator

2. Cancel

** Only a binomial can cancel a binomial.

** Never cancel part of a binomial or part of a trinomial. You can cancel part of a monomial.

## I. Simplifying Monomials:

Example 1  This is actually a review. We already know how to simplify monomials. First, cancel or reduce the coefficients. 10 and 8 reduces to 5 and 4 Second, divide the variables. Remember to subtract exponents when dividing. This is the simplified expression.

Example 2  This is actually a review. We already know how to simplify monomials. First, cancel or reduce the coefficients. 24 and 8 reduces to 3 and 1 Second, divide the variables. Remember to subtract exponents when dividing. This is the simplified expression.

## II. Dividing by a Monomial

Example 3  Divide each term in the numerator by 2x   This is the simplified expression.

Example 4  Divide each term in the numerator by 2x  This is the simplified expression.

Example 5  Divide each term in the numerator by 6 This is the simplified expression.

## III. Dividing by a Binomial or Trinomial

Example 6   Factor the numerator and the denominator.   Cancel the binomials that are identical. (x+1) cancels (x+1)   Do not cancel the remaining x's... never cancel part of a binomial

Example 7   Factor the numerator and the denominator.  Factor Completely   Cancel the 3's and cancel (m+4)

Example 8    Factor the numerator and the denominator.   Factor out 2 in the numerator and -1 in the denominator   Factor Completely   Cancel out ( x - y )