(In addition to this page be sure to copy the examples
given in class!)
A. Reducing a Rational Expression (Section 7.1)
(1) Completely factor the Numerator and Denominator .
(2) Divide out (“Cancel out”) like factors in the Numerator and Denominator.
(3) Write the result.
B. Multiplying Rational Expressions (Section 7.2)
(1) Completely factor each Numerator and Denominator .
(2) Divide out (“Cancel out”) like factors in Numerators and Denominators.
(3) Multiply ( not really ) the factors that remain in the numerators and
(4) Write the result.
C. Dividing Rational Expressions (Section 7.2)
(1) Rewrite the problem as a multiplication problem. Multiply the first rational
expression by the RECIPROCAL of the second rational expression. (A.K.A.:
“Invert and Multiply”)
(2) Proceed as in Multiplication.
D. Adding & Subtracting Rational Expressions (Sections 7.3 and 7.4)
(1) If necessary, completely factor each denominator
(2) Find the Lowest Common Denominator (L.C.D.). Make each denominator “match”
(3) Whatever a denominator is multiplied by, the numerator MUST be multiplied by
the same factor.
(4) Multiply out the expressions in the numerators and place the terms obtained
the L.C.D.. Watch out for NEGATIVE signs . You should now have one big fraction.
(5) Combine like terms in the numerator.
(6) Check to see if the new numerator will factor. If the numerator factors you
be able to reduce the expression.