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)

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