Title: Multiplying and Dividing Rational Expressions
1Section 9.4
- Multiplying and Dividing Rational Expressions
2Multiplying and Dividing Rational Expressions
- A rational expression is considered to be
simplified when its numerator and denominator
have no common factors left
Factor the numerator and denominator...
Example Simplify
Cancel common factors...
2x
Reduce...
3 Multiplying Fractions
(Parenthesize polynomials for clarity) To
Simplify Factor, then cancel like factors
4Example Step by Step
x
1
1
4
1
1
- Write down original problem
- Combine with parenthesized polynomials
- Factor polynomials (if possible)
- Rewrite (if any factoring was done)
- Cancel out matching factors
- Simplify the answer
5Practice - Rational Multiplication
- Write down original problem
- Combine with parenthesized polynomials
- Factor polynomials (if possible)
- Rewrite (if any factoring was done)
- Cancel out matching factors
- Simplify the answer
6Practice - Rational Multiplication
- Write down original problem
- Combine with parenthesized polynomials
- Factor polynomials (if possible)
- Rewrite (if any factoring was done)
- Cancel out matching factors
- Simplify the answer
7Practice - Rational Multiplication
- Write down original problem
- Combine with parenthesized polynomials
- Factor polynomials (if possible)
- Rewrite (if any factoring was done)
- Cancel out matching factors
- Simplify the answer
8Multiplying rational expressions works the same
as multiplying fractionsyou may multiply
numerators and denominators and then simplify, or
you can cross cancel common factors...
Example Multiply
With monomials, its a good idea to multiply
first, and then simplify...
Now reduce...
4
3
4y3 3
9With polynomials, factor each numerator and
denominator, if factorable, and cross cancel to
simplify...
Example Multiply
Factor...
Cross cancel...
x 1 x
10Recall that to divide fractions, you can invert
and multiply ...
Example Divide
Rewrite as multiplication...
Factor...
Cross cancel...
6x2 3x
2x
11Finding Powers of Rational Expressions
- Factor and Simplify (if possible) before applying
the power - If part of a larger expression, see if any terms
cancel out - Usually leave in factored form (unlike the text
example)
12Dividing Fractions
Change to multiplication by reciprocal, then
follow the procedure for multiplication
13Practice - Rational Division
- Write down original problem1a. Rewrite as
multiplication by reciprocal - Combine with parenthesized polynomials
- Factor polynomials (if possible)
- Rewrite (if any factoring was done)
- Cancel out matching factors
- Simplify the answer
14Practice - Rational Division
- Write down original problem1a. Rewrite as
multiplication by reciprocal - Combine with parenthesized polynomials
- Factor polynomials (if possible)
- Rewrite (if any factoring was done)
- Cancel out matching factors
- Simplify the answer
15Practice - Rational Division
- Write down original problem1a. Rewrite as
multiplication by reciprocal - Combine with parenthesized polynomials
- Factor polynomials (if possible)
- Rewrite (if any factoring was done)
- Cancel out matching factors
- Simplify the answer
16Mixed Operations
- Multiplications Division are done left to right
- In effect, make each divisor into a reciprocal
17Assignment
- Section 9.4 page 558 559
- 18 48 (every 3rd)