Title: Rational Expressions
1Rational Expressions Equivalent Forms Here is
the rule
You are allowed to MULTIPLY OR DIVIDE the
numerator and denominator of a fraction by the
SAME constant or variable
2Rational Expressions Equivalent Forms Here is
the rule
You are allowed to MULTIPLY OR DIVIDE the
numerator and denominator of a fraction by the
SAME constant or variable
ADDING / SUBTRACTING the numerator and
denominator of a fraction by the SAME constant or
variable DOES NOT create an equivalent fraction
!!!
3Rational Expressions Equivalent Forms Here is
the rule
You are allowed to MULTIPLY OR DIVIDE the
numerator and denominator of a fraction by the
SAME constant or variable
ADDING / SUBTRACTING the numerator and
denominator of a fraction by the SAME constant or
variable DOES NOT create an equivalent fraction
!!!
When the fractions are simple, cross multiplying
will quickly check for equivalence
4Rational Expressions Equivalent Forms
Example 1 Are these fractions equivalent ?
5Rational Expressions Equivalent Forms
Example 1 Are these fractions equivalent ?
No, if I cross multiply I do not get a true
statement
6Rational Expressions Equivalent Forms
Example 2 Are these fractions equivalent ?
7Rational Expressions Equivalent Forms
Example 2 Are these fractions equivalent ?
YES, because I can MULTIPLY both numerator and
denominator by the same thing to get my result
8Rational Expressions Equivalent Forms
Example 2 Are these fractions equivalent ?
YES, because I can CROSS MULTIPLY and get an
equivalent statement
9Rational Expressions Equivalent Forms
Example 3 Are these fractions equivalent ?
10Rational Expressions Equivalent Forms
Example 3 Are these fractions equivalent ?
YES, because I can cancel the ( b 3 )
anything over itself 1
11Rational Expressions Equivalent Forms
Example 4 Are these fractions equivalent ?
12Rational Expressions Equivalent Forms
Example 4 Are these fractions equivalent ?
NO !!! You can not ADD / SUBTRACT the same thing
from the numerator / denominator and get an
equivalent form