Question

I : Number of partial fractions of $\frac{x^3+x^2+1}{x^4+x^2+1}$ is 4
II : Number of partial fractions of $\frac{3x+5}{(x-1{)}^2(x^2+1{)}^3}$ is 5

Which of the above statement is true.

• A. only I
• B. Only II
• C. Both I and II
• D. Neither I nor II

Answer 1

The correct option is B Only II

statement 1 is false.
$\frac{x^3+x^2+1}{x^4+x^2+1}=\frac{x^3+x^2+1}{(x^2+x+1)(x^2-x+1)}$
$=\frac{Ax+B}{(x^2+x+1)}+\frac{Cx+D}{(x^2-x+1)}$ so two partial fractions.
$\frac{3x+5}{(x-1{)}^2(x^2+1{)}^3}=\frac{A}{(x-1)}+\frac{B}{(x-1{)}^2}+\frac{Cx+D}{(x^2+1)}$
$+\frac{Ex+F}{(x^2+1{)}^2}+\frac{Gx+H}{(x^2+1{)}^3}$
So,$5$ partial fraction
So II correct