Rational Expressions with Fractions in Numerator, Denominator Or Both

Complex Fractions

Complex Fractions  Rational expressions with fractions in numerator, denominator or both  2 methods of simplifying o Method 1: . Simplify numerator . Simplify denominator . Multiply by reciprocal of divisor (denominator) o Method 2: . Find common denominator of the fractions in both numerator and denominator . Multiply complex fraction by the appropriate form of 1

Examples: Simplify Complex Fractions 5 1 Simplify the following n 1 n  3 Method 1: Method 2: Step 1: Simplify numerator & denominator Step 1: Find c.d. between numerator & denominator n 5 n 5  n n  n 3n 3n 1 3n 1  3 3 3

Step 2: Multiply by reciprocal of divisor Step 2: Multiply everything by 3n 5 3n(1) (3n) n 5 3n 1 n 5 3  3n 15    n  1 2 n 3 n 3n 1 (3n)n  (3n) 3n  n 3

Step 3: Simplify and state restrictions Step 3: Simplify and state restrictions 3(n 5) 1 3(n  5) 1 ;n  0, ;n  0, n(3n 1) 3 n(3n 1) 3

Practice: Simplify Complex Fractions 1 1 1 1 1 1 1  1  2  2 1. b a = 2. 2 3. x x 4. x x  0 1 1 1 1 1  1 1 1 b2 a 2 2 x2 x2