# Worksheet: Partial Fraction Expansion: Repeated Linear Factors

In this worksheet, we will practice decomposing a rational fraction whose denominator has repeated linear factors into partial fractions.

**Q1: **

Find and such that .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q3: **

Determine the partial fraction decomposition of .

- A
- B
- C
- D
- E

**Q4: **

Consider the rational expression . The following strategy reveals it as a sum of partial fractions.

What is the value of when ? Let us call this .

So, . What is ? Give the factored and simplified form.

- A
- B
- C
- D
- E

Repeat the first step with and to find and so that . What, finally, is the partial fraction decomposition of ?

- A
- B
- C
- D
- E