What is expand (sec^2(x)(1+x)-tan(x))/((1+x)^2) ?

The solution to expand (sec^2(x)(1+x)-tan(x))/((1+x)^2) is (sec^2(x)+xsec^2(x)-tan(x))/(1+2x+x^2)

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expand (sec^2(x)(1+x)-tan(x))/((1+x)^2)

expand

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

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

Solution steps

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

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

= \frac{sec ^{2} ( x ) ( x + 1 ) - tan ( x )}{1 + 2 x + x ^{2}}

Expand

sec^{2} (x) (1 + x) - tan (x) : sec^{2} (x) + x sec^{2} (x) - tan (x)

= \frac{sec ^{2} ( x ) + x sec ^{2} ( x ) - tan ( x )}{1 + 2 x + x ^{2}}

\frac{( 2 - 3 x ) ^{3}}{( 3 + 2 x ) ^{2}}

\frac{a}{x ( x + a )}

\frac{1}{2 ( p - 12 )}

(c + v^{- 2 t} - 4 e^{t - 2 x})^{2}

2 e^{x} (x - 1)

What is expand (sec^2(x)(1+x)-tan(x))/((1+x)^2) ?
The solution to expand (sec^2(x)(1+x)-tan(x))/((1+x)^2) is (sec^2(x)+xsec^2(x)-tan(x))/(1+2x+x^2)