What is [(2^-x) - 1] divided by [(2^x) - 1] . Solve it.
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calendarEducator since 2008
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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.
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calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
We have to solve (2^-x - 1) / (2^x - 1) = 0
{ Note: It is not possible to solve (2^-x - 1) / (2^x - 1), so I have equated it to 0}
(2^-x - 1) / (2^x - 1) = 0
=> [(1/2^x) - 1]/(2^x - 1) = 0
let 2^x = y
=> [1/y - 1]/[ y - 1] = 0
=>1/y - 1 = 0
=> 1/y = 1
=> y = 1
As y = 2^x, 2^x = 1
=> x = 0
But even with x = 0, the given expression gives 0/0 which is indeterminate.
Therefore, there is no solution.