HW: pg odd, 30 Do Now: Take out your pencil, notebook, and calculator. Objectives: You will be able to simplify rational functions by factoring You will be able to multiply and divide rational fractions. Agenda: 1.Do Now 2.Multiplying and dividing rational functions.

Simplifying, Multiplying, and Dividing Rational Expressions

 A rational expression is written in simplified form when its numerator and denominator share no common factors besides 1.  Simplifying rational expressions uses very similar concepts to those used in simplifying rational numbers (fractions). disappear  It might help to clarify that factors on top and bottom do not disappear, they make a ratio equal to one and therefore divide out.

 To simplify a single rational expression, use the same concepts you would use in simplifying a single fraction.  Look at this example:  The 3’s do not disappear, they make a factor equal to one, which is not necessary to write down.  Apply this same idea to the next examples.

 Simplify each expression:

 Multiplying rational expressions uses the same rules as with multiplying fractions: ◦ Multiply numerators ◦ Multiply denominators ◦ Simplify  We can also try to find common factors in numerators and denominators and divide these out prior to multiplying out.  Look at this example: ◦ Or worked like this: 4 x2x2 y

 Multiply the expressions. Simplify the result.

 To divide one rational expression by another, multiply the first expression by the reciprocal of the second expression.  This is just the same as you would do with two fractions.  Look at this example:

 Divide each expression. Simplify the result.