(x-1)(x^2+x+1)/(x^2+1)(3x^2+4x+5)

Answer 1

Since both factors in the denominator are irreducible quadratics, each numerator will have the form of (Ax+B)

I get

(1/10)(x-3)/(x^2+1) + (1/10)(7x+5)/(3x^2+4x+5)