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Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

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Ineq. #1:

Ineq. #2:

Ineq. #3:

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Ineq. #5:

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Adding and Subtracting Rational Expressions with Different Denominators

Example

Find:

Solution

Step 1 Find the LCD.
Factor each denominator.
The LCD is (x - 1)(x + 3).
Step 2 Rewrite each rational expression with the LCD as the denominator. The denominator of the first fraction is already the LCD.
The denominator of the second fraction needs another factor, (x - 1).
Step 3 Add (or subtract) the numerators. The denominator stays the same.
Add the numerators.
Distribute the 4.
Combine like terms.
Step 4 Reduce to lowest terms.
Factor the numerator.
Cancel the common factor, (x + 3).

So,