SOLUTION: 3) In decomposing 8x-1 / (x+1)(x-2) one of the fractions obtained is: a) 1 / x+1 b) 1 / x-2 c) 5 / x+1 d) 3 / x+1 e) 3 / x-2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 3) In decomposing 8x-1 / (x+1)(x-2) one of the fractions obtained is: a) 1 / x+1 b) 1 / x-2 c) 5 / x+1 d) 3 / x+1 e) 3 / x-2      Log On


   

Question 121738: 3) In decomposing 8x-1 / (x+1)(x-2) one of the fractions obtained is:

a) 1 / x+1
b) 1 / x-2
c) 5 / x+1
d) 3 / x+1
e) 3 / x-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%288x-1%29%2F%28%28x-2%29%28x%2B1%29%29 Start with the given expression.


%288x-1%29%2F%28%28x-2%29%28x%2B1%29%29=A%2F%28x-2%29%2BB%2F%28x%2B1%29 Break up the fraction.


Multiply both sides by the LCD %28x-2%29%28x%2B1%29. Doing this will eliminate every fraction.


8x-1=A%28x%2B1%29%2BB%28x-2%29 Distribute and simplify.

Now let x=2

8%282%29-1=A%282%2B1%29%2BB%282-2%29 Plug in x=2


15=A%283%29%2BB%280%29 Simplify. Notice how the B term is multiplied by zero. So this cancels out B.


15=3A Multiply


15%2F3=A Divide both sides by 3 to isolate A



So our first numerator is A=5


So the first fraction is 5%2F%28x-2%29


However, notice how 5%2F%28x-2%29 is not in the list of answers. So the answer must be the second fraction. So let's solve for B



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Now let x=-1

8%28-1%29-1=A%28-1%2B1%29%2BB%28-1-2%29 Plug in x=-1



-9=A%280%29%2BB%28-3%29 Simplify. Notice how the A term is multiplied by zero. So this cancels out A.



-9=-3B Multiply


-9%2F-3=B Divide both sides by -3 to isolate B



So our second numerator is B=3



So the second fraction is 3%2F%28x%2B1%29





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Answer:


So one of the fractions that %288x-1%29%2F%28%28x-2%29%28x%2B1%29%29 decomposes into is 3%2F%28x%2B1%29



So the answer is D)