The first step in algebraic fractions is to factorise wherever possible.
#color(red)((2a^2+ab-b^2))/color(green)((a^3+b^3)) ÷ color(blue)((2a^2b^2-ab^3))/color(purple)((2a^2-2ab+2b^2))#
#color(red)("quadratic trinomial")/color(green)("sum of cubes") ÷ color(blue)("common factor")/color(purple)("common factor")#
#=color(red)((2a-b)(a+b))/color(green)((a+b)(a^2-ab+b^2)) ÷ color(blue)(ab^2(2a -b))/color(purple)(2(a^2-ab+b^2))#
To divide: multiply by the reciprocal
#=color(red)((2a-b)(a+b))/color(green)((a+b)(a^2-ab+b^2)) xx color(purple)(2(a^2-ab+b^2))/color(blue)(ab^2(2a -b))#
Cancel like factors
#=(cancel((2a-b))cancel((a+b)))/(cancel((a+b))cancel((a^2-ab+b^2))) xx color(purple)(2cancel((a^2-ab+b^2)))/(ab^2cancel((2a -b)))#
#=2/(ab^2)#
