
Adding
and Subtracting
To find the common denominator, I'll first have to factor the quadratic in the third denominator: x^{2} – 5x – 6 = (x – 6)(x + 1) Fortunately for me, the quadratic denominator didn't introduce any new factors to the problem, so the common denominator will be (x – 6)(x + 1). Since I was able to cancel out the x + 1 factor, I eliminated a zero from the denominator. Then the final answer is: Copyright © Elizabeth Stapel 20032011 All Rights Reserved You might not need to include the "for x not equal to –1" part of the solution.
First I'll factor the quadratic in the third denominator: x^{2} + 3x – 10 = (x + 5)(x – 2) Note that these factors almost match the other denominators, but the second fraction's denominator is "backwards". How can I fix that? I can fix it by remembering the following: 5 – 3 = 2 The point of these two
subtractions is that, when I reversed the subtraction, I got the same
answer except for the sign. So I can reverse the subtraction in the
second fraction's denominator, as long as I remember to also reverse
the sign. This is what that looks like:
I factored the numerator, but nothing cancels out. As you can see, I had to factor a denominator, multiply two of the fractions to get a common denominator, multiply those two fractions' numerators, add, simplify, and then factor again. You should expect to see some problems that are at least this involved. They're not as much "complicated" as they are "long and annoying". Work them out stepbystep as I did above, and you'll get the right answers fairly regularly. In this case, the answer is: When you're adding and subtracting rationals, don't try to do a lot of steps in your head, or skip steps or do halfsteps (like leaving out the denominators in your calculations), or you'll pretty much guarantee yourself the wrong answer. Take the time to do every step completely and carefully as you "practice" on the homework, so you have a good chance of getting these exercises right on the test. << Previous Top  1  2  3  Return to Index



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