SOLUTION: Add (x – 7) / (x^2 – 16) + (x – 1) / (16 – x^2)

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Question 215674This question is from textbook Intermediate Algebra
: Add (x – 7) / (x^2 – 16) + (x – 1) / (16 – x^2) This question is from textbook Intermediate Algebra

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x+-+7%29+%2F+%28x%5E2+-16%29++%2B+%28x+-+1%29+%2F+%2816+-+x%5E2%29
As you know, to add fractions we need common denominators. And we prefer the Lowest Common Denominator (LCD).

The key to finding the LCD of %28x%5E2+-+16%29 and %2816+-+x%5E2%29 is to recognize that they are negatives of each other! So we'll start by multiplying the numerator and denominator of the second fraction (or the first, it doesn't matter) by -1:

%28x+-+7%29+%2F+%28x%5E2+-+16%29++%2B+%28-x+%2B+1%29+%2F+%28x%5E2+-+16%29
And with this simple step we have our common denominators! So we're ready to add. The x's in the numerators cancel out and we end up with:
%28-6%29%2F%28x%5E2+-+16%29
This will not reduce so we are finished.

P.S. I don't know what you are using for minus signs but they really mess with Algebra.com's formula rendering software. Please use "normal" minus signs. On a PC keyboard it is right next to zero. Thanks.