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

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

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

expand

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

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

Solution steps

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

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

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

\frac{1}{( z + 1 ) ( z - 1 )}

\frac{( x ^{2} + 5 x + 9 ) ^{n} + x ^{2} ( x + 5 ) ^{2} + 2}{x ^{2} + 5 x + 8}

x ((x - 1) (x - 2))

\frac{d}{d t} ((t) (k (M - t)))

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