chapter 9: rational expressions section 9-1: multiplying and dividing rationals 1.a rational...
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Chapter 9: Rational ExpressionsSection 9-1: Multiplying and Dividing Rationals1. A Rational Expression is a ratio of two polynomial expressions. (fraction)
2. To Simplify a rational expression, look for common factors.
EXAMPLE: Simplify 1
552
x
x
)1)(1(
)1(5
xx
x
1
5
x
- Factor apart what you can.(numerator has a GCF of 5Denominator is a Difference of Squares)
- Cancel common factors of (x – 1) to get your simplified polynomial
3. Remember: When Multiplying fractions, multiply straight across.
** Factor apart what you can, reduce, and multiply across.
EXAMPLE:
y
x
xx
y 1
342
4
y
x
xx
y 1
)1)(3(
4
1
1
)3(
3
xy
)3(
3
xy
- Factor apart any factorable polynomial.
- Reduce
- Multiply Across to get your final result.
4. Remember: Dividing by a fraction is the same as Multiplying by its Reciprocal
EXAMPLE:
2
25
3
152 22
x
x
xx
4
2
3
1522
2
xx
xx
)2)(2(
2
3
)3)(5(
xxx
xx
)2)(2(
2
1
5
xx
x
)2)(2(
)5(2
xx
x
- Multiply by the reciprocal
- Factor what you can
- Reduce
-Multiply across to get the final answer of