The first step is to identify the like terms.
#color(red)(11/6a^2) color(blue)(+2/3a) color(forestgreen)(-1/3ab^3) color(red)(-21/10a^2) color(blue)(-2/3a)color(red)(+19/15a^2)color(forestgreen)(-1/6ab^3+1/2ab^3#
Re-arrange the terms: (not absolutely necessary, but helpful)
#=color(red)(11/6a^2) color(red)(-21/10a^2) color(red)(+19/15a^2)cancelcolor(blue)(+2/3a)cancelcolor(blue)(-2/3a) color(forestgreen)(-1/3ab^3)color(forestgreen)(-1/6ab^3+1/2ab^3#
Notice that the terms in #a# are additive inverses.
Change the fractions to common denominators
#=color(red)(55/30a^2) color(red)(-63/30a^2) color(red)(+38/30a^2) color(forestgreen)(-2/6ab^3)color(forestgreen)(-1/6ab^3+3/6ab^3#
Add the like terms
#=color(red)(30/30a^2 color(forestgreen)(+0/6ab^3)#
#=a^2#
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An alternative method would have been to take out a common factor of #1/30# from each term to start with. This makes all the coefficients whole numbers would get rid of the fractions during the working.
#color(red)(11/6a^2) color(blue)(+2/3a) color(forestgreen)(-1/3ab^3) color(red)(-21/10a^2) color(blue)(-2/3a)color(red)(+19/15a^2)color(forestgreen)(-1/6ab^3+1/2ab^3#
#=1/30(color(red)(55a^2) cancelcolor(blue)(+2/3a) color(forestgreen)(-10ab^3) color(red)(-63a^2) cancelcolor(blue)(-2/3a)color(red)(+38a^2)color(forestgreen)(-5ab^3+15ab^3))#
Simplify like terms inside the bracket:
#=1/30(color(red)(30a^2) color(forestgreen)(+0ab^3))#
Multiplying gives #a^2#
