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Partial Fractions Q. (1 Viewer)

namburger

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( x^2 + x + 2 ) / x(x+1)

My working out:

( x^2 + x + 2 ) / x(x+1) = A / x + B / (x+1)

x^2 + x + 2 = A (x+1) + Bx
Let x = -1
2 = -B
B = -2

Let x = 0
A = 2

Therfore
( x^2 + x + 2 ) / x(x+1) = 2 / x - 2 / (x+1)

However the answer says it is 1 + 2 / x - 2 / (x+1)
I found out the correct method to do this is long divide it first, and you should get the correct answer. Why do we need to divide for? What did i do wrong in my Working out
 

leoyh

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you have to long divide first because the power of x is the same on top and bottom. thats when you have to long divide first. if its for example, x on the top but x^2 on the bottom, then you can just do it directly

the answer should be 1 + (2/x) + (-2 / x+1)
 

Slidey

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namburger said:
x^2 + x + 2 = A (x+1) + Bx
The error is here:

Should be:

( x^2 + x + 2 ) / x(x+1) = A / x + B / (x+1) + C
x^2+x+2=Ax+A+Bx+Cx^2+Cx
C=1
A+B+C=1
A=2
Thus B=-2

1 + 2/x - 2/(x+1)

Alternatively, as leoyh said:
(x^2+x+2)/(x^2+x) = 1 + 2/(x^2+x), and go from there:
2=A(x+1)+Bx
A=2
A+B=0
B=-2
 
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