Question

Hi guys pl show it step by step..!​

Answer 1

$\sf{Prove \: that : \bf\dfrac{2^{x-1}+2^x}{2^{x+1} { - 2}^{x} }=\dfrac{3}{2}}$

let,

$\sf{LHS= \dfrac{2^{x-1}+2^x}{2^{x+1} { - 2}^{x} }}$

$\sf{RHS= \dfrac{3}{2}}$

• On solving LHS we get

$\sf{~~~~~:\implies LHS= \dfrac{2^{x-1}+2^x}{2^{x+1} { - 2}^{x} }}$

• Taking 2^{x} common

$\sf{~~~~~:\implies LHS= \dfrac{ {2}^{x} (2^{-1}+1)}{2 ^{x} (2^{1} - 1 )}}$

$\sf{~~~~~:\implies LHS= \dfrac{ \dfrac{1}{2} +1}{2 - 1 }}$

$\sf{ ~~~~~:\implies LHS= \dfrac{ \dfrac{2 + 1}{2}}{1 }}$

$\sf{~~~~~:\implies LHS= \dfrac{3}{2} \times 1}$

$\sf{~~~~~:\implies LHS= \dfrac{3}{2} }$

${ \bf \: LHS= RHS }~~_{verified}$