What is expand (8x-42)/((x^2+1)^3) ?

The solution to expand (8x-42)/((x^2+1)^3) is (8x-42)/(x^6+3x^4+3x^2+1)

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expand (8x-42)/((x^2+1)^3)

expand

\frac{8 x - 42}{( x ^{2} + 1 ) ^{3}}

\frac{8 x - 42}{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}

Solution steps

\frac{8 x - 42}{( x ^{2} + 1 ) ^{3}}

(x^{2} + 1)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1

= \frac{8 x - 42}{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}

\frac{1}{32} (12 x + 8 sin (2 x) + sin (4 x)) + C

\frac{1}{3} (12 d + e)

2 (x - i y)^{2}

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

(a + bi)^{3}

What is expand (8x-42)/((x^2+1)^3) ?
The solution to expand (8x-42)/((x^2+1)^3) is (8x-42)/(x^6+3x^4+3x^2+1)