Question

power series by using partial fractions: f(x)=(x+2)/(2x^2-x-1)

Answer 1

\[(x+2)/((x-1)(2x+1))=(x+1)(x-1)^{-1}(2x+1)^{-1}\] if |x|>1 then

Answer 2

\[(x+1)x ^{-1}(1-1/x)^{-1}(2x)^{-1}(1+1/2x)^{-1}=(x+1)(1-1/x)^{-1}(1+1/2x)^{-1}/2x ^{2}\]

or if |x|<1/2 then the expression would be as it is given if 1/2<|x|<1
then\[(x+2)(x-1)^{-1}(1+2x)^{-1}/2x\]now you can use the formula of binomial series and u will get the required power series.