Trigonometric Identities

Prove:
(tanx + secx -1)/(tanx - secx + 1)= tanx + secx

My work so far:

(sinx/cosx + 1/cosx + cosx/cosx)/(sinx/cos x - 1/cosx + cosx/cosx)= tanx + cosx

(just working on the left side)
((sinx + 1 - cosx)/cosx)/((sinx - 1 + cosx)/cosx)

((sinx + 1 - cosx)/cos x) x (cos x/(sinx - 1 + cosx))

(sinx + 1 - cosx)/(sinx - 1 + cosx)

here is where I get stuck. Could someone point me in the right direction?

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