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

The solution to expand (2(t^2+1-2t))/((t^2+1)^2) is (2t^2+2-4t)/(t^4+2t^2+1)

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

expand

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

\frac{2 t ^{2} + 2 - 4 t}{t ^{4} + 2 t ^{2} + 1}

Solution steps

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

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

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

Expand

2 (t^{2} + 1 - 2 t) : 2 t^{2} + 2 - 4 t

= \frac{2 t ^{2} + 2 - 4 t}{t ^{4} + 2 t ^{2} + 1}

\frac{5 ( 5 + 65 )}{4}

\frac{( a + b ) ( a - b )}{2 a ( 1 - b )}

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

(- i, - 2 j, 3 k) \cdot (- 3 i, 0 j, k)

\frac{7 x ^{2} + 5 x + 7}{( x - 2 ) ( x ^{2} + 2 x + 1 )}

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