What is expand (2^{2x+2})/((4^x+1)^2) ?

The solution to expand (2^{2x+2})/((4^x+1)^2) is (2^{2x+2})/(16^x+2^{1+2x)+1}

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expand (2^{2x+2})/((4^x+1)^2)

expand

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

\frac{2 ^{2 x + 2}}{1 6 ^{x} + 2 ^{1 + 2 x} + 1}

Solution steps

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

(4^{x} + 1)^{2} = 1 6^{x} + 2^{1 + 2 x} + 1

= \frac{2 ^{2 x + 2}}{1 6 ^{x} + 2 ^{2 x + 1} + 1}

(1 - 7) + (7 - 7)

\frac{( s + 3 )}{( s + 2.5 ) ( s + 4 ) ^{2}}

\frac{( s + 1 ) ( s - 2 )}{( s + 3 )}

\frac{6 x ^{2} + 41 x - 17}{( x + 2 ) ( x + 8 ) ( x + 5 )}

\frac{- 0.5 n z ^{n} - 0.5 z ^{n} + n z ^{n + 1}}{( z - 0.5 ) ^{2}}

What is expand (2^{2x+2})/((4^x+1)^2) ?
The solution to expand (2^{2x+2})/((4^x+1)^2) is (2^{2x+2})/(16^x+2^{1+2x)+1}