Derivation of the equation to determine the concentration of carbonic acid components by [DIC] and [H+] (review)

In the previous problem, we derived an equation for the percentage of each carbonic acid component to [DIC] at a given pH. Please prepare paper and pencil and transform the following equation to state [HCO₃^-] = (function of [DIC] and [H+])

Equation (1)　[DIC] = [HCO₃^-] + [CO₃^2-] + [H₂CO₃] 　　　　　

Equation (3)　　　K1 = [HCO₃^-]・[H⁺]／[H₂CO₃] 

Equation (4)　　　K2 = [CO₃^2-]・[H⁺]／[HCO₃^-] 

Equation (6)  [HCO₃^-]=     ~~        ←(function of [DIC] and [H+])

Substitute this into Equations (3) and (4),

Equation (7) [H₂CO₃]=     ~~        ←(function of [DIC] and [H+])

Equation (8) [CO₃^2-]=      ~~        ←(function of [DIC] and [H+])

The result is as such.

The "~~" part should be determined by each of you and written on a piece of paper.