What is expand (derivative of 2x+1)/((x+1)^2) ?

The solution to expand (derivative of 2x+1)/((x+1)^2) is (derivative of 2x+1)/(x^2+2x+1)

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expand (derivative of 2x+1)/((x+1)^2)

expand

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

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

Solution steps

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

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

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

\frac{1}{( s ^{2} + 2 s + 2 )} (\frac{1}{( s + 1 ) ^{2}})

e^{2 x} + e^{- 2 x} (2 e^{2 x} + 2 e^{- 2 x})

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

(1 + \frac{1}{8 n}) x^{2} - 2 x + 1

(x - 2 + 8)^{2}

What is expand (derivative of 2x+1)/((x+1)^2) ?
The solution to expand (derivative of 2x+1)/((x+1)^2) is (derivative of 2x+1)/(x^2+2x+1)