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

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) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

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 how the B term is multiplied by zero. So this cancels out B.

Multiply

Divide both sides by 3 to isolate A

So our first numerator is

So the first fraction is

However, notice how is not in the list of answers. So the answer must be the second fraction. So let's solve for B

--------------------------------------------------------------------------------

Now let

Plug in

Simplify. Notice how the A term is multiplied by zero. So this cancels out A.

Multiply

Divide both sides by -3 to isolate B

So our second numerator is

So the second fraction is

--------------------------------------------------------------------------------

Answer:

So one of the fractions that decomposes into is

So the answer is D)

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