Adding and Subtracting Simple Fractions With Variables

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ADDING AND SUBTRACTING FRACTIONS WITH VARIABLES

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To add or subtract fractions:

You must have a common denominator.
To find the Least Common Denominator (LCD),
take the least common multiple of the individual denominators.
Express each fraction as a new fraction with the common denominator,
by multiplying by one in an appropriate form.
To add fractions with the same denominator:
add the numerators, and keep the denominator the same.
That is, use the rule:

AC +BC =A+ BC

EXAMPLE:
Combine into a single fraction: 2x +3-3 xx-1

Solution: Note that the LCD is (x+3) (x-1) .

2x +3-3 xx-1	(original expression)
=  2x +3⋅ x-1x- 1- 3 xx-1 ⋅ x+3 x+3	(get a common denominator by multiplying by 1 )
=  2(x-1 )-3x(x +3)(x +3)(x- 1)	(keep the denominator the same; add the numerators)
=  2x- 2-3x 2-9x (x+3) (x-1)	(multiply out the numerator)
=  -3x2 -7x-2 (x+3) (x-1)	(combine like terms; write numerator in standard form)

Leave the denominator in factored form for your final answer.

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.

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