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)

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) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Factor the denominator.

Break up the fraction.

Multiply both sides by the LCD . Doing this will eliminate every fraction.

Distribute and simplify.

Now let

Plug in

Simplify. Notice the B term goes away

Divide both sides by -2 to solve for A

So one numerator is which means the first fraction is

However since the fraction is not in the list, this means the second fraction must be in the list

Now let

Plug in

Simplify. Notice the A term goes away

Divide both sides by 2 to solve for B

So another numerator is which means the second fraction is

---------------------------
Answer:

So this shows us that the answer is which means the choice is E)
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