Algebraic Fractions Section 0.6 Objectives: 1) Simplify an algebraic fraction. 2) Multiply and divide algebraic fractions 3) Add and subtract algebraic fractions 4) Simplify complex fractions

College Algebra Section 1.6 Terms: If x and y are real numbers, y  0, then x/y is called a fraction. x is the numerator y is the denominator Algebraic fractions are fractions containing algebraic expressions. If the algebraic expressions are polynomials then the fraction is called a rational expression. College Algebra Section 1.6

Two fractions are equal if their cross products are equal. because 2a(6) = 3(4a) Is ? No, because(3x2)(16x2)  (4y2)(12y2) College Algebra Section 1.6

College Algebra Section 1.6 To Simplify Fractions - divide out all factors that are common to both numerator and denominator Ex.1 Ex.2 College Algebra Section 1.6

Multiplying and Dividing Fractions Multiply: numerator x numerator denominator x denominator Divide out common factors Divide: Multiply by the reciprocal of the divisor College Algebra Section 1.6

Multiplying Algebraic Fractions College Algebra Section 1.6

Dividing Algebraic Fractions- Write the reciprocal and multiply. College Algebra Section 1.6

Adding and Subtracting Algebraic Fractions Factor the denominator, if necessary Find the LCD (least common denominator) The LCD can be found by using each factor the greatest number of times that it appears in any one denominator. Write each fraction as an equivalent fraction with this LCD. College Algebra Section 1.6

Adding and Subtracting with unlike Denominators College Algebra Section 1.6

Subtracting Algebraic Fractions with Unlike Denominators College Algebra Section 1.6

College Algebra Section 1.6 Complex Fraction Is a fraction that has a fractional numerator and/or a fractional denominator. Two ways to simplify complex fractions: 1) Multiply numerator and denominator of the complex fraction by the LCD 2) Combine fractions in the numerator and combine fractions in the denominator and then divide the two fractions. College Algebra Section 1.6

Simplify the complex fraction College Algebra Section 1.6