SOLUTION: (x-7)/(x-8)-(x+1)/(x+8)+(x-24)/(x^2-64) Perform the indicated operations and simplify?

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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): You can put this solution on YOUR website!
 
Hi,
(x^2-64) = (x-8)(x+8) the LCD

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
*************
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.
***********
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.
***************
Ex:

Because 4*3 = 12, multiply 1st fraction by 3, 2nd by 4, and 3rd by 1.
**************
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
***************
Note:
(x+a)(x+b) = x^2 + (a+b)x + ab
*****************

**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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