Question 468027: (x-7)/(x-8)-(x+1)/(x+8)+(x-24)/(x^2-64)
Perform the indicated operations and simplify?
Found 2 solutions by ewatrrr, ccs2011:
Answer by ewatrrr(24785)   (Show Source):
Answer by ccs2011(207)  (Show Source):
You can put this solution on YOUR website! 
Factor 
This is an example of difference of squares
Next find common denominator
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Ex:
The common denominator is the least common multiple of 3,4,12
Since 3 and 4 are both factors of 12 then the LCM is 12.
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In the same way, (x-8) and (x+8) are factors of (x-8)(x+8)
Thus the LCM and common denominator is (x-8)(x+8).
However, the value of the expression cannot change, if the denominator changes then the numerator must change by the same factor.
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Ex:
Because 4*3 = 12, multiply 1st fraction by 3, 2nd by 4, and 3rd by 1.
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In the same way, multiply 1st fraction by (x+8), 2nd by (x-8), 3rd by 1.
Since denominators are now the same, combine into one fraction
Distribute on top and add like terms
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Note:
(x+a)(x+b) = x^2 + (a+b)x + ab
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**Be careful when subtracting and remember to distribute the negative sign**
Factor the 9 since it is a common factor to both 9 and 72
Cancel like factors both on top and bottom of a fraction
Therefore leaving the solution
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