# Rational Expressions Chapter 14 Chapter Sections 14.1  Simplifying Rational Exp

## Rational Expressions Chapter 14 Chapter Sections 14.1  Simplifying Rational Exp

Richardson, Hamilton, Millbrook Reporter has reference to this Academic Journal, PHwiki organized this Journal Rational Expressions Chapter 14 Chapter Sections 14.1  Simplifying Rational Expressions 14.2  Multiplying in addition to Dividing Rational Expressions 14.3  Adding in addition to Subtracting Rational Expressions with the Same Denominator in addition to Least Common Denominators 14.4  Adding in addition to Subtracting Rational Expressions with Different Denominators 14.5  Solving Equations Containing Rational Expressions 14.6  Problem Solving with Rational Expressions 14.7  Simplifying Complex Fractions § 14.1 Simplifying Rational Expressions

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Rational Expressions To evaluate a rational expression as long as a particular value(s), substitute the replacement value(s) into the rational expression in addition to simplify the result. Evaluating Rational Expressions Example Evaluate the following expression as long as y = 2. In the previous example, what would happen if we tried to evaluate the rational expression as long as y = 5 This expression is undefined! Evaluating Rational Expressions

We have to be able to determine when a rational expression is undefined. A rational expression is undefined when the denominator is equal to zero. The numerator being equal to zero is okay (the rational expression simply equals zero). Undefined Rational Expressions Find any real numbers that make the following rational expression undefined. The expression is undefined when 15x + 45 = 0. So the expression is undefined when x = 3. Undefined Rational Expressions Example Simplifying a rational expression means writing it in lowest terms or simplest as long as m. To do this, we need to use the Fundamental Principle of Rational Expressions If P, Q, in addition to R are polynomials, in addition to Q in addition to R are not 0, Simplifying Rational Expressions

Simplifying a Rational Expression 1) Completely factor the numerator in addition to denominator. 2) Apply the Fundamental Principle of Rational Expressions to eliminate common factors in the numerator in addition to denominator. Warning! Only common FACTORS can be eliminated from the numerator in addition to denominator. Make sure any expression you eliminate is a factor. Simplifying Rational Expressions Simplify the following expression. Simplifying Rational Expressions Example Simplify the following expression. Simplifying Rational Expressions Example

Simplify the following expression. Simplifying Rational Expressions Example § 14.2 Multiplying in addition to Dividing Rational Expressions Multiplying Rational Expressions Multiplying rational expressions when P, Q, R, in addition to S are polynomials with Q 0 in addition to S 0.

Multiplying Rational Expressions Note that after multiplying such expressions, our result may not be in simplified as long as m, so we use the following techniques. Multiplying rational expressions 1) Factor the numerators in addition to denominators. 2) Multiply the numerators in addition to multiply the denominators. 3) Simplify or write the product in lowest terms by applying the fundamental principle to all common factors. Multiplying Rational Expressions Multiply the following rational expressions. Example Multiplying Rational Expressions Multiply the following rational expressions. Example

Dividing Rational Expressions Dividing rational expressions when P, Q, R, in addition to S are polynomials with Q 0, S 0 in addition to R 0. Dividing Rational Expressions When dividing rational expressions, first change the division into a multiplication problem, where you use the reciprocal of the divisor as the second factor. Then treat it as a multiplication problem (factor, multiply, simplify). Dividing Rational Expressions Divide the following rational expression. Example

Units of Measure Converting Between Units of Measure Use unit fractions (equivalent to 1), but with different measurements in the numerator in addition to denominator. Multiply the unit fractions like rational expressions, canceling common units in the numerators in addition to denominators. Units of Measure Convert 1008 square inches into square feet. (1008 sq in) Example § 14.3 Adding in addition to Subtracting Rational Expressions with the Same Denominator in addition to Least Common Denominators

Rational Expressions If P, Q in addition to R are polynomials in addition to Q 0, Adding Rational Expressions Add the following rational expressions. Example Subtracting Rational Expressions Subtract the following rational expressions. Example

Subtracting Rational Expressions Subtract the following rational expressions. Example Least Common Denominators To add or subtract rational expressions with unlike denominators, you have to change them to equivalent as long as ms that have the same denominator (a common denominator). This involves finding the least common denominator of the two original rational expressions. Least Common Denominators To find a Least Common Denominator: 1) Factor the given denominators. 2) Take the product of all the unique factors. Each factor should be raised to a power equal to the greatest number of times that factor appears in any one of the factored denominators.

Simplifying Complex Fractions Example Simplifying Complex Fractions Method 2 as long as simplifying a complex fraction Find the LCD of all the fractions in both the numerator in addition to the denominator. Multiply both the numerator in addition to the denominator by the LCD. Simplify, if possible. Simplifying Complex Fractions Example

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