Page 625 - Algebra 1

The product of a number and its reciprocal is 1. To eliminate the fraction in the denominator of a complex fraction, multiply the numerator and the denominator by the reciprocal of the denominator.
Simplifying Using the Reciprocal of the Denominator
Example
2
Simplify _x . mn
SOLUTION
_ _n _x
=
=
_ _
am
mn
am · mn
_ _
nx x ·mn
_ _n
am
Multiply by the reciprocal of the denominator.
Divide out common factors.
Multiply. Simplify.
_ Factoring to Simplify _3x
_x + 12 Simplify 6 . 9
x+2 S_OLUTION
_3x
mn x am · mn
_ _ nx
x ·mn _ _
mn x
_2
_
= x 1
am
_2
= am x
Example
3
6
= =
= =
__ 3x ÷ 9
Write using a division symbol.
Factor out the GCF and multiply by the reciprocal.
Divide out common factors. Simplify.
_x + 1 2 9 x+2
6x + 12 x + 2 3x · x + 2
__ 6(x + 2) 9
31x · (x + 2) __
6(x + 2) 9
_x 18
3
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610 Saxon Algebra 1