SOLUTION: 14) In decomposing 7x-8/x^2-2x using partial fraction techniques, one fraction obtained is a) 4/x+2 b) 4/x-2 c) 3/x d) 3/x+2 e)

Algebra ->  Trigonometry-basics -> SOLUTION: 14) In decomposing 7x-8/x^2-2x using partial fraction techniques, one fraction obtained is a) 4/x+2 b) 4/x-2 c) 3/x d) 3/x+2 e)       Log On


   

Question 122543: 14) In decomposing 7x-8/x^2-2x using partial fraction techniques, one fraction obtained is

a) 4/x+2
b) 4/x-2
c) 3/x
d) 3/x+2
e) 3/x-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%287x-8%29%2F%28x%5E2-2x%29 Start with the given expression.


%287x-8%29%2F%28x%28x-2%29%29 Factor the denominator.


%287x-8%29%2F%28x%28x-2%29%29=A%2F%28x%29%2BB%2F%28x-2%29 Break up the fraction.


Multiply both sides by the LCD x%28x-2%29. Doing this will eliminate every fraction.


7x-8=A%28x-2%29%2BB%28x%29 Distribute and simplify.



Now let x=0

7%280%29-8=A%280-2%29%2BB%280%29 Plug in x=0


-8=-2A Simplify. Notice the B term goes away


4=A Divide both sides by -2 to solve for A


So one numerator is A=4 which means the first fraction is 4%2Fx


However since the fraction 4%2Fx is not in the list, this means the second fraction must be in the list




Now let x=2

7%282%29-8=A%282-2%29%2BB%282%29 Plug in x=0


6=2B Simplify. Notice the A term goes away


3=B Divide both sides by 2 to solve for B


So another numerator is B=3 which means the second fraction is 3%2F%28x-2%29


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Answer:

So this shows us that the answer is 3%2F%28x-2%29 which means the choice is E)