Question

Number of partial fractions obtained $\frac{3x-5}{(x+1{)}^3(x^2+1{)}^2}$

• A. 5
• B. 4
• C. 6
• D. 3

Answer 1

The correct option is A 5

$\frac{3x-5}{(x+1{)}^3(x^2+1{)}^2}=\frac{A}{(x+1)}+\frac{B}{(x+1{)}^2}+\frac{C}{(x+1{)}^3}+\frac{Dx+E}{(x^2+1)}$
$+\frac{fx+9}{(x^2+1{)}^2}$
$3x-5=A(x+1{)}^2(x^2+1{)}^2+B(x+1)(x^2+1{)}^2$
$+C(x^2+1{)}^2+(Dx+E\left)\right(x^2+1\left)\right(x+1{)}^3+f\left(x\right)+g(x+1{)}^3$
So, there are 5 partial fractions.
$\frac{A}{x+1}+\frac{B}{(x+1{)}^2}+\frac{C}{(x+1{)}^3}+\frac{Dx+E}{(x^2+1)}+\frac{f\left(x\right)+g}{(x^2+1{)}^2}$
5 Partial fractions