SOLUTION: I'm not sure how to work this could someone help me please. 11/x^2-4-8/x+2 (/= over)directions are subtract and simplify if possible.

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Question 172045: I'm not sure how to work this could someone help me please.
11/x^2-4-8/x+2 (/= over)directions are subtract and simplify if possible.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I think that the expression you were trying to render looks something like:

%2811%2F%28x%5E2-4%29%29-%288%2F%28x%2B2%29%29

And I will proceed on that basis.

In order to subtract fractions, you need a common denominator. You can always find a common denominator simply by multiplying all of your denominators together, but if your denominators have common factors, you can create a Lowest Common Denominator (LCD) that will simplify your work.

But what factor(s) do x%5E2-4 and x%2B2 have in common? Look closely at your first denominator. Do you recognize the 'difference of two squares' pattern? Do you recall from your study of factoring quadratic polynomials the rule for factoring the difference of two squares?

Remember: a%5E2-b%5E2=%28a%2Bb%29%28a-b%29.

Therfore: x%5E2-4=%28x%2B2%29%28x-2%29.

But look: Now you can see that x%5E2-4 and x%2B2 have the factor x%2B2 in common. Hence, the LCD is simply x%5E2-4.

Let's apply the common denominator to the original expression:

%2811%2F%28x%5E2-4%29%29-%288%28x-2%29%2F%28x%2B2%29%28x-2%29%29

%2811%2F%28x%5E2-4%29%29-%288%28x-2%29%2F%28x%5E2-4%29%29%29

Distribute, collect like terms, and add the numerators:

%2811-8x%2B16%29%2F%28x%5E2-4%29%29%29

%2827-8x%29%2F%28x%5E2-4%29%29%29

Done