Question

how do I resolve into partial fractions: 3x^2-8x+1/(x-4)(x^2+1)

Answer 1

synthetic division first

Answer 2

I think synthetic division is not required here,
the degree of numerator is already less than the denominator.

so we do this:
\(\Large \dfrac{3x^2-8x+1}{(x-4)(x^2+1)}=\dfrac{A}{x-4}+\dfrac{Bx+C}{x^2+1}\)

let me know if you need help in finding A,B,C.
@salii99

Answer 3

hint: make common denominator on right side,
and then compare co-efficients of the numerators on both sides.