What is expand-(2x(-x^2+189))/((x^2+63)^3) ?

The solution to expand-(2x(-x^2+189))/((x^2+63)^3) is -(-2x^3+378x)/(x^6+189x^4+11907x^2+250047)

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expand-(2x(-x^2+189))/((x^2+63)^3)

expand

- \frac{2 x ( - x ^{2} + 189 )}{( x ^{2} + 63 ) ^{3}}

- \frac{- 2 x ^{3} + 378 x}{x ^{6} + 189 x ^{4} + 11907 x ^{2} + 250047}

Solution steps

- \frac{2 x ( - x ^{2} + 189 )}{( x ^{2} + 63 ) ^{3}}

(x^{2} + 63)^{3} = x^{6} + 189 x^{4} + 11907 x^{2} + 250047

= - \frac{2 x ( - x ^{2} + 189 )}{x ^{6} + 189 x ^{4} + 11907 x ^{2} + 250047}

Expand

2 x (- x^{2} + 189) : - 2 x^{3} + 378 x

= - \frac{- 2 x ^{3} + 378 x}{x ^{6} + 189 x ^{4} + 11907 x ^{2} + 250047}

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

(e^{\frac{x}{2}} + e^{- \frac{x}{2}})^{2}

2 (7 + 4)

(1 + tan (x)) (1 - tan (x)) sec^{2} (x)

What is expand-(2x(-x^2+189))/((x^2+63)^3) ?
The solution to expand-(2x(-x^2+189))/((x^2+63)^3) is -(-2x^3+378x)/(x^6+189x^4+11907x^2+250047)