How do you do partial fraction $\frac2{x^2 - 8}$? How do you do partial fraction on $\frac2{x^2 - 8}$ ? Or are there other method of doing? I tried trig substitution but could not get the answer.

By using Maple, you can find the fractions in @Adi's answer easily.
 [> evalf(convert(2/(x^2-8),parfrac,x,real),2);

                            -.36/(x+2.8)+.36/(x-2.8)

The square factor $(x^2-8)$ does not factor over the integers.
