Question

simplify 2^X+1 + 2^X / 2^X+1 - 2^x​

Answer 1

$\frac{ {2}^{x + 1} + {2}^{x} }{ {2}^{x + 1} - {2}^{x} } \\ = > \frac{ {2}^{x} \times {2}^{1} + {2}^{x} }{ {2}^{x} \times {2}^{1} - {2}^{x} } \\ on \: taking \: {2}^{x} common \: in \: both \: numerator \: and \: denominator \: we \: get \: \\ = > \frac{{2}^{x} (2 + 1)}{ {2}^{x} (2 - 1 )} \\ = > \frac{ {2}^{x} \times 3}{ {2}^{x} \times 1} \\ = > 3$

THERE YOU GO!!!.....

Answer 2

2^(x+1) - 2^(1-x) =1

2^x*2 - 2/2^x = 1

Let say 2^x =y,then

2y - 2/y =1

Multiplying both sides by y,we get

2y^2 -2=y

2y^2- y - 2=0

y=[1+-sqrt(1+16)]/4

y=[1+-sqrt(17)]/4

2^x=[1+-sqrt(17)]/4

But 2^x >1

So,2^x= [1+sqrt(17)]/4