We need to simplify the expression (2^-x -1) / (2^x -1)
First , we will rerite 2^-x = 1/2^x
==> (2^-x) -1= (1/2^x) -1 = (1-2^x)/2^x= -(2^x-1)/2^x
Now we will substitute into the expression.
==> (2^-x)-1)/ (2^x -1) = (-2^x-1)/2^x] / (2^x-1)
Now we will reduce similar terms.
==> -1/2^x / 1 -1/2^x
==> (2^-x)-1) / (2^x-1) = -1/2^x = -2^-x
Now we will try and find the solution.
==> -1/2^x = 0
Then, there is no solution for the equation because the numerator is a constant numbers and can not be zero.
Then, there is no solution.