how to work out partial fraction decomposition when given

Question

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

if you could give me an idea of the formula and what changes i need to make to the formula when the denominator changes that would help and please use idiot speak because the text books are confusing me

Answer 1

i think i worked out the second one but i still cant do the first

is it = 9/7(x+4)+5/7(x-3)???