Write the terms for partial fraction decomposition but don't solve for constants.
Hint
First factor the denominator. Then write your sum of terms with constants A, B, C over each factor.
Answer
Example 2
Write the terms for partial fraction decomposition but don't solve for constants of:
Hint
Write each fraction for the x4 factor starting at power of 1 to the power of 4, then take care of the (x + 2) factors similarly, then the (x2 + 9).
Answer
Example 3
Expand this algebraic fraction into partial fractions. Solve for the constants.
Hint
First factor the x2 – 9 in the denominator. Set up three partial fractions with A, B and C. Clear the fractions, then try substituting in x = 3, x = -3 and x = 0 in to solve for the constants.
Answer
Example 4
Using partial fractions, decompose this algebraic fraction:
Hint
Setup the two partial fractions with A and B constants. Try 2 values of x to setup a system of equations. You won't find any x values that cancel out a term, so you will have to solve with matrices.
Answer
Example 5
Use matrices to get partial fractions of:
Hint
Set up constants, then clear fractions. Then try using x = 0 and x = 1. Setup a system of equations to solve for A and B. Solve using inverse matrices. So many steps, such little time.
