SOLUTION: a) f(x)= x^2-1/x(x=2) find the partial fraction of f(x) b) Solve f(x)>0, hence write the solution for f(x)<0 Solution of the question need show in line and also table as well.

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Question 621023: a) f(x)= x^2-1/x(x=2)
find the partial fraction of f(x)
b) Solve f(x)>0, hence write the solution for f(x)<0
Solution of the question need show in line and also table as well.
tq.
Answer by Edwin McCravy(20086)   (Show Source): You can put this solution on YOUR website!
f(x) =  

When the degree of the numerator is greater than or equal to the
degree of the denominator, the fraction must be divided out first
by long division:

  = 

                      1
x² - 2x + 0)x² - 0x - 1
            x² - 2x + 0
                 2x - 1

f(x) = 1 +  = 1 + 

f(x) = 1 +  = 1 +  + 

 =  + 

2x-1 = A(x-2) + Bx

This must be true for all values of x so we choose x=2
so the first term on the right will be 0

2(2)-1 = A(2-2) + B(2)
 4 - 1 = A(0) + 2B
     3 = 0 + 2B
     3 = 2B
      = B

Now we choose x=0 so the second term on the right will be 0

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

 +  =  +  = · + · =  + 

Therefore f(x) =  = 1 +  + 


Edwin