Rational Expressions

1
Rational 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
2
Rational 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
!!!
3
Rational 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
4
Rational Expressions Equivalent Forms
Example 1 Are these fractions equivalent ?
5
Rational Expressions Equivalent Forms
Example 1 Are these fractions equivalent ?
No, if I cross multiply I do not get a true
statement
6
Rational Expressions Equivalent Forms
Example 2 Are these fractions equivalent ?
7
Rational 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
8
Rational Expressions Equivalent Forms
Example 2 Are these fractions equivalent ?
YES, because I can CROSS MULTIPLY and get an
equivalent statement
9
Rational Expressions Equivalent Forms
Example 3 Are these fractions equivalent ?
10
Rational Expressions Equivalent Forms
Example 3 Are these fractions equivalent ?
YES, because I can cancel the ( b 3 )
anything over itself 1
11
Rational Expressions Equivalent Forms
Example 4 Are these fractions equivalent ?
12
Rational 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