Question

Step by step explanation
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Answer 1

Question:-

Prove that

$\frac{ {2}^{x - 1} + {2}^{x} }{ {2}^{x + 1} - {2}^{x} } = \frac{3}{2}$

Required Formula:-

${a}^{m - n} = \frac{ {a}^{m} }{ {a}^{n} }$

${a}^{m + n} = {a}^{m} \times {a}^{n}$

Solution:-

Take LHS

By using formulae

LHS becomes

=$\frac{ (\frac{ {2}^{x} }{2}) + {2}^{x} }{( {2}^{x} \times 2) - {2}^{x} }$

Take 2^x in common

=$\frac{ {2}^{x} ( \frac{1}{2} + 1) }{ {2}^{x} (2 - 1)}$

=$\frac{ \frac{1 + 2}{2} }{1}$

=$\frac{3}{2}$

So, LHS = RHS

Hence, proved

Answer 2

Step-by-step explanation:

Here's ur answer in the above attachment