Let us consider the following rational function:

$f(x)=\frac{37x^2+8x+17}{x^3-x^2+x-1}$

$($i$)$ What is the corrct form to find the partial fractions of $f(x)$

$\frac{37x^2+8x+17}{x^3-x^2+x-1}=\frac{A}{x-1}+\frac{C}{x^2+1}$

$\frac{37x^2+8x+17}{x^3-x^2+x-1}=\frac{A}{x+1}+\frac{Bx+C}{x^2+1}$

$\frac{37x^2+8x+17}{x^3-x^2+x-1}=\frac{A}{x-1}+\frac{Bx+C}{x^2+1}$

$\frac{37x^2+8x+17}{x^3-x^2+x-1}=\frac{A}{x-1}+\frac{Bx}{x^2+1}$

$($ii$)$ Write the partial decomposition of this rational function:

Answer:

$\frac{37x^2+8x+17}{x^3-x^2+x-1}=$