SOLUTION: Please help me anyone with this question. I have triedm it over and over again and it is just getting confusing. PLEASE HELP ME!!!!!! 1)x^2-12x+32/x^2-6x-16/x^2-x-12/x^2-5x-24

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me anyone with this question. I have triedm it over and over again and it is just getting confusing. PLEASE HELP ME!!!!!! 1)x^2-12x+32/x^2-6x-16/x^2-x-12/x^2-5x-24      Log On


   

Question 116949: Please help me anyone with this question. I have triedm it over and over again and it is just getting confusing. PLEASE HELP ME!!!!!!
1)x^2-12x+32/x^2-6x-16/x^2-x-12/x^2-5x-24
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%28%28x%5E2-12x%2B32%29%2F%28x%5E2-6x-16%29%29%2F%28%28x%5E2-x-12%29%2F%28x%5E2-5x-24%29%29
.
This is how I interpret what you meant in your problem.
.
Recall way back in your days of learning about fractions ... you learned that if you divide
by a fraction it is the same as inverting that fraction and multiplying it by the quantity you
are trying to divide it into.
.
In this problem you are trying to divide the very bottom fraction:
.
%28%28x%5E2-x-12%29%2F%28x%5E2-5x-24%29%29
.
Into the very top fraction:
.
%28%28x%5E2-12x%2B32%29%2F%28x%5E2-6x-16%29%29
.
Following the fraction rule of division, you can invert the very bottom fraction into the form:
.
%28%28x%5E2-5x-24%29%2F%28x%5E2-x-12%29%29
.
and multiply it by the very top fraction to make the original division problem become the
following equivalent multiplication problem:
.
%28%28x%5E2-12x%2B32%29%2F%28x%5E2-6x-16%29%29%2A%28%28x%5E2-5x-24%29%2F%28x%5E2-x-12%29%29
.
Now let's do lots of factoring as follows:
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x%5E2-12x%2B32=%28x-8%29%2A%28x-4%29
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x%5E2-6x-16=%28x-8%29%2A%28x%2B2%29
.
x%5E2-5x-24+=+%28x-8%29%2A%28x%2B3%29
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and finally:
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x%5E2-x-12=+%28x-4%29%2A%28x%2B3%29
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Substituting these factor into the appropriate places in the equivalent multiplication
problem results in that problem becoming:
.

.
Now carefully go through the problem and, as much as you can, cancel a factor in the numerator
with a corresponding factor somewhere in the denominator. This should look like this:
.

.
And what you are left with is the answer:
.
%28x-8%29%2F%28x%2B2%29
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Hope this helps you to work your way through this problem.
.