What is sqrt(1+e^x)*sqrt(1+(e^{2x))/(4(1+e^x))} ?

The solution to sqrt(1+e^x)*sqrt(1+(e^{2x))/(4(1+e^x))} is sqrt((e^x+1)((e^{2x))/(4(e^x+1))+1)}

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simplify sqrt(1+e^x)*sqrt(1+(e^{2x))/(4(1+e^x))}

simplify

1 + e^{x} \cdot 1 + \frac{e ^{2 x}}{4 ( 1 + e ^{x} )}

(e^{x} + 1) (\frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1)

Solution steps

1 + e^{x} 1 + \frac{e ^{2 x}}{4 ( 1 + e ^{x} )}

Apply radical rule:

a b = a \cdot b,

assuming

a \geq 0, b \geq 0

e^{x} + 1 \frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1 = (e^{x} + 1) (\frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1)

= (e^{x} + 1) (\frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1)

(- 144)^{- \frac{3}{2}}

(\frac{2}{3})^{- 5^{^{'}}}

2 x (e^{- x})

(6.6726 \cdot 1 0^{- 11}) (3.17 \cdot 1 0^{7})

\frac{( x ^{2} + 1 ) ^{4}}{x ^{4}}

What is sqrt(1+e^x)*sqrt(1+(e^{2x))/(4(1+e^x))} ?
The solution to sqrt(1+e^x)*sqrt(1+(e^{2x))/(4(1+e^x))} is sqrt((e^x+1)((e^{2x))/(4(e^x+1))+1)}