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 Monday 16th of September

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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 2’s 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

FIND LCD

2m-4 2(m-2)

3m-6 3(m-2)

LCD is then 2 * 3 * (m-2)

the restrictions on m are m cannot be 2.