9.1 Multiplying and Dividing Rational Expressions Algebra II w/ trig

Rational Expression: a ratio of two polynomial expressions ◦To simplify a rational expression, divide both numerator and denominator by their GCF ◦ This means you will need to factor all polynomials that are factorable. ◦A rational expression is in simplest form if its numerator and denominator have no common factors

Multiply Rational Expressions: if b ≠ 0 and d ≠ 0 Dividing Rational Expressions: if b ≠ 0, c ≠ 0 and d ≠ 0

I. Simplify each expression. A.B. C.D.

E.F. G.H.

II. Multiply and Simplify. A.B. C.Multiply then reduce, OR cross cancel/ reduce then multiply.

When numerators and/or denominators are factorable … - Factor - Cancel out common factors in num/den - Multiply and leave answer in factored form. D.

E. F.

III. Divide and Simplify - Change division to multiplication - Flip the second fraction - Factor each piece if possible - Cancel out common factors in num/den - Multiply and leave answer in factored form A.

B.C.

D.E.

IV. Complex Fractions (fraction within a fraction) - Rewrite as a division expression then use the steps for division. A.

B.C.