What is expand (-x^6+3x^2)/((x^4+1)^2) ?

The solution to expand (-x^6+3x^2)/((x^4+1)^2) is (-x^6+3x^2)/(x^8+2x^4+1)

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expand (-x^6+3x^2)/((x^4+1)^2)

expand

\frac{- x ^{6} + 3 x ^{2}}{( x ^{4} + 1 ) ^{2}}

\frac{- x ^{6} + 3 x ^{2}}{x ^{8} + 2 x ^{4} + 1}

Solution steps

\frac{- x ^{6} + 3 x ^{2}}{( x ^{4} + 1 ) ^{2}}

(x^{4} + 1)^{2} = x^{8} + 2 x^{4} + 1

= \frac{- x ^{6} + 3 x ^{2}}{x ^{8} + 2 x ^{4} + 1}

(\frac{3 n}{3 n + 1}) - (\frac{3 n - 3}{3 n - 2})

6 (6 d + 8 e) + 2 (2 d - 9 e)

- \frac{7 s + 2 s ^{3}}{( s ^{2} + 4 ) ^{2}}

(1, 3, - 2) x (- 1, 5, 7)

\frac{( n + 1 ) ( n + 2 ) ( 4 n + 3 )}{3}

What is expand (-x^6+3x^2)/((x^4+1)^2) ?
The solution to expand (-x^6+3x^2)/((x^4+1)^2) is (-x^6+3x^2)/(x^8+2x^4+1)