What is expand ((1-sin(x)+t^2)t)/((1+t^2)^2) ?

The solution to expand ((1-sin(x)+t^2)t)/((1+t^2)^2) is (t-tsin(x)+t^3)/(1+2t^2+t^4)

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expand ((1-sin(x)+t^2)t)/((1+t^2)^2)

expand

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

\frac{t - t sin ( x ) + t ^{3}}{1 + 2 t ^{2} + t ^{4}}

Solution steps

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

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

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

Expand

(1 - sin (x) + t^{2}) t : t - t sin (x) + t^{3}

= \frac{t - t sin ( x ) + t ^{3}}{1 + 2 t ^{2} + t ^{4}}

(2 cos (x) - 1) (2 cos (x) + 1)

4 (x + h) - 3 - 4 x - 3

x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

\frac{d}{d x} (x^{4} - 2 x^{3} - 4 x^{2} - 5 x + 2)

(\frac{1}{x} - x) (y - \frac{1}{y})

What is expand ((1-sin(x)+t^2)t)/((1+t^2)^2) ?
The solution to expand ((1-sin(x)+t^2)t)/((1+t^2)^2) is (t-tsin(x)+t^3)/(1+2t^2+t^4)