What is expand (e^x(1+x^2)-2xe^x)/((1+x^2)^2) ?

The solution to expand (e^x(1+x^2)-2xe^x)/((1+x^2)^2) is (e^x+e^xx^2-2e^xx)/(1+2x^2+x^4)

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expand (e^x(1+x^2)-2xe^x)/((1+x^2)^2)

expand

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

\frac{e ^{x} + e ^{x} x ^{2} - 2 e ^{x} x}{1 + 2 x ^{2} + x ^{4}}

Solution steps

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

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

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

Expand

e^{x} (1 + x^{2}) - 2 x e^{x} : e^{x} + e^{x} x^{2} - 2 x e^{x}

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

(x - 25) (x + 25)

(n + 1)!

- 2 (\frac{1}{5} cot^{5} (\frac{x}{2}) + \frac{1}{3} cot^{3} (\frac{x}{2})) + C

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

(x - 3 i)^{2}

What is expand (e^x(1+x^2)-2xe^x)/((1+x^2)^2) ?
The solution to expand (e^x(1+x^2)-2xe^x)/((1+x^2)^2) is (e^x+e^xx^2-2e^xx)/(1+2x^2+x^4)