#lim _(x->a) (x^3/8-a^3/8)/(x^5/3-a^5/3)#
As we can easily recognize that this is #0/0# we'll modify the fraction
#((x^3-a^3)*3)/((x^5-a^5 )*8)#
Apply the factoring rule
#(cancel(x -a)(a^2+ax+x^2)*3)/(8cancel(x-a)(x^4+x^3a+ x^2a^2+xa^3+a^4)#
Plug in the value a
#((a^2+aa+a^2)*3)/(8(a^4+a^3a+ a^2a^2+aa^3+a^4)#
#((3a^2)*3)/(8(2a^4+2a^3a^1+ a^2a^2)#
#(9a^2) /(8(2a^4+2a^4+ a^4)#
#(9a^2) /(8(5a^4)#
#(9a^2) /(40a^4)#
#= (9) /(40a^(4-2))#
#= (9) /(40a^(2))#
#lim _(x->a) (x^3/8-a^3/8)/(x^5/3-a^5/3)=(9) /(40a^(2)) #
