Multiplying and Dividing Rational Expressions

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Multiplying and Dividing Rational Expressions Section 8.2 in Textbook

Rational Expression – a quotient of two polynomials Examples: or or Simplify rational expressions in the same way as you simplify fractions. Divide out common factors in the numerator and denominator

Simplifying Rational Expressions You will be asked to simplify expressions and then determine values for which the expression would be undefined… Undefined expressions – when the denominator of an expression equals ZERO!?! Must use ORIGINAL denominator (not reduced form) to find these answers.

Examples: Simplify. Identify any x-values for which the expression is undefined. (Use original denominator!!) A. B. C.

Multiplying Rational Expressions Factor all the numerators and denominators completely. Divide out common factors of numerators and denominators. Multiply numerators. Then multiply denominators. Be sure the numerator and denominator have no common factors other than 1.

Examples: D. E.

Examples: F. G.

Dividing Rational Expressions To divide fractions, you must … Multiply by its reciprocal?? Keep, change, flip?? Keep the first fraction Change the sign to multiply Flip the second fraction Apply multiplication rules after the problem has been set up!!

Examples: H. J.

Examples: K.

Your Turn Simplify. Identify any x-values for which the expression is undefined. 1. 2. Multiply or Divide. Assume all expressions are defined. 3. 4. 5. 6.

Solving Simple Rational Equations Simplify the numerator and denominator - factor out any common terms Solve for x… Make sure to look for excluded values – they can lead to a NO SOLUTION!?!

Examples: M. N. P. Q.