Question

The number of partial fraction of $\frac{x^2+3x+1}{(x-1{)}^5}$ is

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (C)

3

By substitution $x-1=t$
$x=t+1$
$\frac{(t+1{)}^2+3(t+1)+1}{t^5}$ substituting in the above eqn.
$\frac{t^2+5t+5}{t^5}=1/t^3+5/t^4+5/t^5$
$=1/(x-1{)}^3+5/(x-1{)}^4+5/(x-1{)}^5$
3 partial fractions