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Multiplying and Dividing Rational Expressions
I. Rational Expressions and Functions
A. A rational expression is a polynomial divided by a
B. A rational function is a function defined by a formula that is a rational expression.
C. Fractions are rational expressions.
What value(s) of x would make the denominators of the
above examples equal to 0?
Why do these values matter ?
Examples: Find the domain of the following functions. (Easiest to use set-builder notation.)
B. To simplify:
1) Factor completely the numerator and denominator .
2) Divide both the numerator and denominator by the common factors; that is, cancel out any
common factors that the numerator and denominator share. NEVER cancel TERMS ; only FACTORS.
III. Multiplying Rational Expressions
A. Multiplying rational expressions is the same as multiplying fractions:
B. To multiply rational expressions:
1) Factor completely all numerators and denominators.
2) Divide numerators and denominators by common factors.
3) Multiply the remaining numerators; multiply the remaining denominators.
IV. Dividing Rational Expressions
A. Dividing rational expressions is the same as dividing fractions:
C. To divide rational expressions:
1) Leave the first rational expression alone; change division to multiplication; “flip” the divisor.
2) Now it is a multiplication problem. Proceed with multiplication.