Dividing and Subtracting Rational Expressions
Lowest common denominators
What is the LCD for the following: 8,4,6
8 - 2 * 2 * 2
4 - 2 * 2
6 - 2 * 3
what is common from all three? three 2s are common from
each with a 2 left over, so the LCD is 2 * 2 * 2 * 3 = 24
5a - 5 * a
2a 2 - 2 * a * a
a 3 - a * a * a
LCD 5 * 2 * a * a * a = 10a 3
the other way of thinking about it is to decide what can I do
to each term so they look alike?
Adding and subtracting with monomial denominators
4/5a - 3/2a 2 + 1/a 3
The LCD is 10a 3.
With that information we know what the denominator is going to
be. Now what do we have to do to each term in order from them to
equal 10a 3?
from here we can add or
subtract the numerators at will.
the final solution is:
the final solution must
also include the RESTRICTIONS.
Restrictions are the values that the denominator can not
take(values which will make it zero). In this case the only
values it cannot take are when a is equal to zero.
Common binomial factors
LCD is then 2 * 3 * (m-2)
the restrictions on m are m cannot be 2.