find the domain

Question

f(x)=x/x-8,g(x)=-7/x

solve the following exponential equation equation exact answers only
3e x-1 = 2+e^x-1

Answer 1

domain of any rational function is all reals except where the denominator is zero.

dom(f) = all reals except x=8
dom(g) = all reals except x=0

If you meant
3e^x-1 = 2+e^(x-1)
3e^x - e^x/e = 2+1
e^x (3-1/e) = 3
e^x = 3/(3-1/e)
x = ln3e - ln(3e-1)

If, however, you meant
3e^(x-1) = 2+e^(x-1)
2e^(x-1) = 2
e^(x-1) = 1
x-1 = 0
x = 1

If something else, then you'd better repost with proper parentheses.