Mathematics
Find the partial fraction decompostion of the rational function

### Question Description

8 divided by ( x minus 1)(x plus1)       8/(x-1)(x+1)

8/(x-1)(x+1)

step 1_  8/(x-1)(x+1) = A/(x-1) + B/(x+1)...................1

step 2_   multiply (x-1)(x+1) on both sides, we get

step 3_   8 = A(x+1) + B(x-1)

step 4_   put   x+1=0   or   x = -1 we get

step 5_   8 = A(-1+1) + B(-1-1)

step 6_   8 = A(0) + B(-2)

step 7_   8 = -2B

Step 8_  Divide by -2 on both sides, we get

step 9_  B = -4

step 10_  put  x-1=0  or  x=1  we get

step 11_  8 = A(1+1) + B(1-1)

step 12_   8 = 2A + B(0)

step 13_  8 = 2A

step 14_  Divide by 2 on both sides we get

step 15_   A = 4

step 16_   now put the values of A and B in equation 1, we get

step 17_   8/(x-1)(x+1) = 4/(x-1) - 4/(x+1)

HENCE ,  WE GET

8/(x-1)(x+1)  =  4/(x-1) - 4/(x+1)

University of Virginia
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