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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

\frac{7}{( 4 + x ) ^{3}}

e^{2 t} t^{\frac{1}{5}} + t u (t - 4)

cot (a) (sin (a) + tan (a))

\frac{2 ( s ^{2} + 1 )}{s ^{2} ( s ^{2} + 5 )}

5^{4}

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