Question

Resolve 1/(x-1)^2(x-2) into partial fractions

Answer 1

Answer:

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Answer 2

1/(x - 1) (x + 1)  =  A/(x - 1) + B/(x + 1)

1/(x - 1) (x + 1)  =  A(x + 1) + B(x - 1)/(x - 1)(x + 1)

Since we have same denominators on both side, we can equate the numerators.

1  =  A(x + 1) + B(x - 1)  ------(1)

The constants A and B can also be found by successively giving suitable values for x.

To find A, put x = 1 in (1)

To find B, put x = -1 in (1)

1  =  A(1 + 1) + B(1 - 1)

1 = 2A + B (0)

1 = 2A + 0

2A  =  1  ===> A = 1/2  

1  =  A(-1 + 1) + B(-1 - 1)

1 = A(0) + B (-2)

1 = 0 - 2B

-2B  =  1  ===> B = -1/2