Can you please help me with this Calculus problem

I got this question wrong on my quiz.

I took a screen cap of it. I need help on the question I highlighted (c). Can someone show me the steps?

The question:
http://i48.tinypic.com/5y6kpz.png

My professor told me the answer is : y= 2+((12)/(x+1))
But I don't know how to get to it

x = 4e^t - 1
y = 3e^-t + 2

so when we leave e^t alone in the first equation :
e^t = (x + 1) / 4

we place this in the second equation with the y but since it's e^-t ---> it means 1 / e^t
so that means y = 3 (1/e^t) + 2

and if we place e^t there in the y equation:
y = 3 [1/ ((x + 1) / 4))] + 2
y = 3 (4 / (x + 1)) + 2

and that is y = (12 / (x + 1)) + 2

phew :) hope it wasn't all over the place ask if you have a question.

x = 4e^(t) - 1 ---> solve for t
x + 1 = 4e^(t)
(x + 1)/4 = e^(t)
ln( (x + 1)/4 ) = t

y = 2 + 3e^( - t ) ---> having ln( (x + 1)/4 ) = t

y = 2 + 3e^( - ln( (x + 1)/4 ) )
y = 2 + 3e^( ln( ((x + 1)/4 ))^-1 )
y = 2 + 3e^( ln( 4/(x + 1) )
y = 2 + 3 * ( 4/(x + 1) )
y = 2 + ( 12/(x + 1) )

Note:
2 ln(x) --- can be written as ln(x^2)

e^ln(x) -----> x

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free to e-mail if have a question

Part C:

x(t) = -1 + 4e^(t) and y(t) = 2 + 3e^(-t)

(x + 1)/4 = e^(t) => e^(-t) = 4/(x + 1)

y = 2 + 12/(x + 1)