What is expand-(3ur^3(ux^3+ur^3))/(x^7) ?

The solution to expand-(3ur^3(ux^3+ur^3))/(x^7) is -(3u^2r^3)/(x^4)-(3u^2r^6)/(x^7)

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expand-(3ur^3(ux^3+ur^3))/(x^7)

expand

- \frac{3 u r ^{3} ( u x ^{3} + u r ^{3} )}{x ^{7}}

- \frac{3 u ^{2} r ^{3}}{x ^{4}} - \frac{3 u ^{2} r ^{6}}{x ^{7}}

Solution steps

- \frac{3 u r ^{3} ( u x ^{3} + u r ^{3} )}{x ^{7}}

Expand

3 u r^{3} (u x^{3} + u r^{3}) : 3 u^{2} r^{3} x^{3} + 3 u^{2} r^{6}

= - \frac{3 u ^{2} r ^{3} x ^{3} + 3 u ^{2} r ^{6}}{x ^{7}}

Apply the fraction rule:

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

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

= - (\frac{3 u ^{2} r ^{3} x ^{3}}{x ^{7}}) - (\frac{3 u ^{2} r ^{6}}{x ^{7}})

Remove parentheses:

(a) = a

= - \frac{3 u ^{2} r ^{3} x ^{3}}{x ^{7}} - \frac{3 u ^{2} r ^{6}}{x ^{7}}

Cancel

\frac{3 u ^{2} r ^{3} x ^{3}}{x ^{7}} : \frac{3 u ^{2} r ^{3}}{x ^{4}}

= - \frac{3 u ^{2} r ^{3}}{x ^{4}} - \frac{3 u ^{2} r ^{6}}{x ^{7}}

\frac{3 x ^{2} + 40}{x ( 100 - x )}

(e^{x} cos (2 x)) \cdot (e^{x} sin (2 x) + 2 e^{x} cos (2 x))

\frac{1}{( x - 9 ) ^{2}}

l im x \Rightarrow - 1 (x - 2 [∣ x ∣])

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

What is expand-(3ur^3(ux^3+ur^3))/(x^7) ?
The solution to expand-(3ur^3(ux^3+ur^3))/(x^7) is -(3u^2r^3)/(x^4)-(3u^2r^6)/(x^7)