Multiplying and Dividing Rational Expressions
Ι Multiplying Rational Expressions
To MULTIPLY rational expressions, factor all polynomials and reduce first, then
multiply numerators by numerators and denominators by denominators. [Always
check the result to see if it will reduce to simpler form.]
Caution: You can cancel only complete factors. You cannot cancel a piece of a sum.
You cannot cancel the 5 in the fraction
nor the â€œxâ€ in the expression
NOTE: Look at all of the polynomials in the rational expressions
and start factoring
the ones you recognize first. You can use these to help factor the others using
the â€œtrial and errorâ€ method. If all else fails you always use the GN (grouping
number) method to factor. Reduce the factored expressions and collect factors.
If binomial differences have the letters in opposite order, factor out
(1).
Examples
1)
2)
ΙΙ Dividing Rational Expressions
To DIVIDE by a rational expression,
CHANGE TO MULTIPLY by the INVERSE, or (reciprocal).
Examples
1)
Change to MULTIPLY:
Factor
Reduce
2)
Change to MULTIPLY:
Factor:
Reduce:
