Power series expansion involving non integer exponent I'm working on a real and complex analysis course right now and one power series question has me really stumped:

I'm not sure what to do with the non integer in the exponent, as my initial plan of differentiating the power series of 1/(1-x) won't work.
Any help on this would be great, thanks!

I do not see what is the problem after Olivier Oloa's answer (use the generalized binomial theorem).
Doing so, the series expansion you look for is, around $x=a$ $$\frac{1}{(1-x)^{3/2}}=\frac{1}{(1-a)^{3/2}}+\frac{3 (x-a)}{2 (1-a)^{5/2}}+\frac{15 (x-a)^2}{8
   (1-a)^{7/2}}+\frac{35 (x-a)^3}{16 (1-a)^{9/2}}+O\left((x-a)^6\right)$$
