Systems of Equations Exercises

Example 1

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.

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).

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.

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.

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.

Systems of Equations Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

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