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Rational Expressions and Their Simplification
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Simplifying Algebraic Expressions
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Rational Expressions Worksheet
Adding and Subtracting Rational Expressions
Rational Expressions
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Dividing Fractions, Mixed Numbers, and Rational Expressions
Multiplying and Dividing Rational Expressions
Multiplying and Dividing Rational Expressions
Simplifying Rational Expressions
Complex Rational Expressions
Rational Expressions and Equations
Integration of Polynomial Rational Expressions
Algebraic Expressions
Radical Expressions & Radical Functions
Rational Class and Expression Evaluator
Adding and Subtracting Rational Expressions
Rational Expressions
Radical Expressions
Multiplying Rational Expressions
Rational Expressions and Common Denominators
rational expressions
Polynomial Expressions
Rational Functions, and Multiplying and Dividing Rational Expressions
Simplifying Radical Expressions
Adding and Subtracting Rational Expressions
Rational Expressions and Equations
Rational Expressions
RATIONAL EXPRESSIONS II
Simplifying Expressions
Quadratic Expressions,Equations and Functions
RATIONAL EXPRESSIONS
Absolute Value and Radical Expressions,Equations and Functions
Rational Expressions & Functions

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rational expressions

Complex rational expressions contain fractions within fractions. This is un-
desirable. We now learn how to turn complex rational expressions into the
preferable rational expression.

When would we encounter such a situation?
If  and consider , Then

We will learn two ways of accomplishing our goal. You may choose the one
you prefer.

Property 0.1 Simplify a Complex Rational Expresion by Multiplying by


1. Find the LCD of all rational expressions within the complex rational
expression.

2. Multiply both the numerator and denominator of the complex rational
expression by this LCD.

3. Use the distributive property and multiply each term in the numera-
tor and denominator by the LCD. Simplify each term. No fractional
expressions should remain within the main fraction.

4. Factor and simplify.

Example 0.1

Property 0.2 Simplify a Complex Rational Expresion by Dividing

1. Add or subtract to get a single expression in the numerator.

2. Add or subtract to get a single expression in the denominator.

3. Perform the division indicated by the main fraction bar. That is, invert
the denominator of the complex rational expression and multiply.

4. Simplify.

Example 0.2 Simplify a Complex Rational Expresion by Dividing

Example 0.3 Suppose Find

Example 0.4 If three resistors with resistances R1, R2, and R1 are con-
nected in parrallel, their combined resistance, R, is given by the formula

Simplify the complex rational expression on the right side of the formula.
Then  find R, to the nearest hundredth of an ohm, when R1 is 4 ohms, R2 is
8 ohms, and R3 is 12 ohms.

when R1 is 4 ohms, R2 is 8 ohms, and R3 is 12 ohms