What is expand-(3x(-2x^2+9))/((x^2+3)^{7/2)} ?

The solution to expand-(3x(-2x^2+9))/((x^2+3)^{7/2)} is (6x^3)/((x^2+3)^{7/2)}-(27x)/((x^2+3)^{7/2)}

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expand-(3x(-2x^2+9))/((x^2+3)^{7/2)}

expand

- \frac{3 x ( - 2 x ^{2} + 9 )}{( x ^{2} + 3 ) ^{\frac{7}{2}}}

\frac{6 x ^{3}}{( x ^{2} + 3 ) ^{\frac{7}{2}}} - \frac{27 x}{( x ^{2} + 3 ) ^{\frac{7}{2}}}

Solution steps

- \frac{3 x ( - 2 x ^{2} + 9 )}{( x ^{2} + 3 ) ^{\frac{7}{2}}}

Expand

3 x (- 2 x^{2} + 9) : - 6 x^{3} + 27 x

= - \frac{- 6 x ^{3} + 27 x}{( x ^{2} + 3 ) ^{\frac{7}{2}}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 6 x ^{3} + 27 x}{( x ^{2} + 3 ) ^{\frac{7}{2}}} = - (- \frac{6 x ^{3}}{( x ^{2} + 3 ) ^{\frac{7}{2}}}) - (\frac{27 x}{( x ^{2} + 3 ) ^{\frac{7}{2}}})

= - (- \frac{6 x ^{3}}{( x ^{2} + 3 ) ^{\frac{7}{2}}}) - (\frac{27 x}{( x ^{2} + 3 ) ^{\frac{7}{2}}})

Remove parentheses:

(a) = a, - (- a) = a

= \frac{6 x ^{3}}{( x ^{2} + 3 ) ^{\frac{7}{2}}} - \frac{27 x}{( x ^{2} + 3 ) ^{\frac{7}{2}}}

A (8, 3) B (1, - 4)

\frac{( 3 x ^{2} - 11 x - 62 )}{( x ^{2} - 4 ) ( x + 1 )}

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

(3 - 2)^{5}

What is expand-(3x(-2x^2+9))/((x^2+3)^{7/2)} ?
The solution to expand-(3x(-2x^2+9))/((x^2+3)^{7/2)} is (6x^3)/((x^2+3)^{7/2)}-(27x)/((x^2+3)^{7/2)}