Rate Law Problem

[chemoly]

The reaction of tert-butyl bromide with azide ion in
aqueous solution is proposed to proceed by the following
mechanism:

(CH3)3CBr(aq) ⇌ (CH3)3C+(aq) + Br–(aq)
where k 1 is the forward reaction and k -1 is the reverse reaction

(CH3)3C+(aq) + N3–(aq) -> (CH3)3CN3(aq)
k2 is the rate constant

Assuming that (CH3)3C+(aq) achieves a steady-state
concentration, but making no further assumptions about
the relative magnitudes of the three rate constants, what is
the rate law for this reaction?

The answer is Rate = {k1k2[(CH3)3CBr][N3–]}/{k–1[Br–] + k2[N3–]}

But how would I obtain that answer using multistep reaction mechanisms and not differential equations??

Thanks so much!