Split Using Partial Fraction Decomposition 4/(x(x-1))

Problem

4/(x*(x−1))

Solution

1. Set up the partial fraction decomposition by assigning a constant to each linear factor in the denominator.

4/(x*(x−1))=A/x+B/(x−1)

2. Clear the fractions by multiplying both sides of the equation by the common denominator x*(x−1)

4=A*(x−1)+B*x

3. Solve for A by substituting x=0 into the equation to eliminate the B term.

4=A*(0−1)+B(0)

4=−A

A=−4

4. Solve for B by substituting x=1 into the equation to eliminate the A term.

4=A*(1−1)+B(1)

4=B

B=4

5. Substitute the values of A and B back into the original decomposition form.

4/(x*(x−1))=(−4)/x+4/(x−1)

Final Answer

4/(x*(x−1))=4/(x−1)−4/x

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