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Simplify the following: (5x - 1)/(x + 8) - (3x + 4)/(x + 8) These fractions already have a common denominator, so I can just add. But I'll use parentheses on the numerators, to make sure I carry the "minus" through the second parentheses. (A common mistake would be to take the "minus" sign only onto the "3x" and not onto the "4".) (5x - 1)/(x + 8) - (3x + 4)/(x + 8) = (2x - 5)/(x + 8) Then the answer is: (2x - 5)/(x + 8) Simplify the following: 3x/(x^2 + 3x - 10) - 6/(x^2 + 3x - 10) Again, these already have a common denominator, so I can just combine them as they are. But the denominator is a quadratic, so I'll want to factor the numerator when I'm done, to check and see if anything cancels out. 3x/(x^2 + 3x - 10) - 6/(x^2 + 3x - 10) = [3(x - 2)]/[(x + 5)(x - 2)] = 3/(x + 5) As you can see, something did cancel. You always need to remember this step: factor the denominator and numerator (if possible) and check for common factors. By the way, since I was able to cancel off the "x – 2" factor, this eliminated a zero from the denominator. Depending on your book and on your instructor, you may (or may not) need to account for this change in the domain of the fraction. Copyright © Elizabeth Stapel 2003-2011
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