We are learning series and I really need help with this. I can't find any help with these, could someone please help? Thanks!

Question

Answer 1

The denominator factors as (1-x)(1+3x)

Solve the identity x≡[A(1-2x)]+[B/(1-3x)] tp get A=1/5=-B

Form 2 partial fractions.

Now divide the two fractions by long division and add them to get the coefficients required.

Don't forget the facor of 25 and the common factor 1/5 in the A and B.