Lesson 1: 7-1 Multiplying and Dividing Rational Expressions

1. How is dividing polynomials similar to multiplying fractions?
2. Why can it be good to start fresh and rewrite a polynomial division answer when you have made a mistake and cannot easily find your error?
3. What is a nonpermissible value?
4. Why is it nonpermissible?

Rational Expression
Complex Fraction

A.APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, and multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

SAT questions related to rational functions: 1-3-13, 6-3-12

The primary skill needed to multiply and divide rational expressions is simplifying. After division is changed to multiplication by the reciprocal of the divisor, and numerators and denominators are multiplied, complete the problem by dividing by the common factors.

If a scuba diver goes to depths greater than 33 feet, the rational function T(d)=1700/(d-33) gives the maximum time a diver can remain at those depths and still surface at a steady rate with no stops. T(d) represents the dive time in minutes and d represents the depth in feet.

Point out that rational expressions are usually used without specifically excluding those values that make the expression undefined. It is understood that only those values for which the expression has meaning are included.

Encourage students to use several steps, writing each one below the previous and keeping each line equivalent to the one above. Caution them to make only one change per step.

McGraw Hill resources

McGraw Hill resources