(%i1) hgfred([1/2,1/2],[3/2],-(%i*(x-%i))/(2*(1-%i*(x-%i))));
(%o1) (sqrt((%i*(x-%i))/(2*(1-%i*(x-%i)))+1)*asin(sqrt(-(%i*(x-%i))/(2*(1-%i*(x-%i))))))/(sqrt(-(%i*(x-%i))/(2*(1-%i*(x-%i))))*sqrt(1--(%i*(x-%i))/(2*(1-%i*(x-%i)))))
(%i2) expand(%,0,0);
(%o2) (sqrt(2)*asin(sqrt(-(%i*(x-%i))/(1-%i*(x-%i)))/sqrt(2)))/sqrt(-(%i*(x-%i))/(1-%i*(x-%i)))