Question

proove that 2^x-1+2^x/2^x+1-2^x=3/2

Answer 1

Answer :

Now,

L.H.S. = {2^(x - 1) + 2^x} / {2^(x + 1) - 2^x}

= [{2^x × 2^(-1)} + 2^x]/[{2^x × 2^(1)} - 2^x]

= {2^x (1/2 + 1)}/{2^x (2 - 1)}

= (3/2)/1

= 3/2

= R.H.S. [Proved]

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Answer 2

solution:-

given by:-

$\frac{ {2}^{x - 1} + {2}^{x} }{ {2}^{x + 1} - {2}^{x} } = \frac{3}{2} \\ \frac{ {2}^{x}( {2}^{ - 1} + 1) }{ {2}^{x} ( {2}^{1} - 1)} = \frac{3}{2} \\ \frac{ \frac{1}{2} + 1}{1} = \frac{3}{2} \\ \frac{1 + 2}{2} = \frac{3}{2} \\ \frac{3}{2} = \frac{3}{2} \\( lhs = rhs)proved$