You can put this solution on YOUR website! Given to simplify:
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Since these are "setup" problems that are designed to teach a point, you can make a guess
that the numerator and the denominator have a common term that cancels out.
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Let's re-write the numerator that it is arranged in descending powers of x ... that is
so the x term appears first followed by the constant. When we do that the problem becomes:
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Then in the numerator, factor out so that we make the term positive. This makes the
expression become:
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Now let's see if we can factor the denominator. And let's guess that one of the factors
might be . This being the case we might begin the factoring with:
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We know that times has to equal the of the given denominator. Therefore, will have to equal so that . So go to our factored form of the denominator
and substitute for to make the factored form:
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Note that when we do the next step we just write the as
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Next from this factored form we can see that if we multiply the constant by
B, it has to result in the of the original denominator of the problem. So we can
say that:
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and we can solve this for B by multiplying both sides by to get:
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Substitute this value for B in the factored form of our denominator and you have that the
factored form is:
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You can check this out by doing the multiplication just to be sure that the product is
equal to the original denominator.
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Substitute this into the problem where we had rearranged the numerator and we now have:
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Cancel the common factor in the numerator with the same factor in the denominator:
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And you are left with the simplified form:
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and that's your answer.
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Hope this explanation helps you to understand the problem.
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