What is expand (3(2x^5-xy^2+2))/(x^3) ?

The solution to expand (3(2x^5-xy^2+2))/(x^3) is 6x^2-(3y^2)/(x^2)+6/(x^3)

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expand (3(2x^5-xy^2+2))/(x^3)

expand

\frac{3 ( 2 x ^{5} - x y ^{2} + 2 )}{x ^{3}}

6 x^{2} - \frac{3 y ^{2}}{x ^{2}} + \frac{6}{x ^{3}}

Solution steps

\frac{3 ( 2 x ^{5} - x y ^{2} + 2 )}{x ^{3}}

Expand

3 (2 x^{5} - x y^{2} + 2) : 6 x^{5} - 3 x y^{2} + 6

= \frac{6 x ^{5} - 3 x y ^{2} + 6}{x ^{3}}

Apply the fraction rule:

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

\frac{6 x ^{5} - 3 x y ^{2} + 6}{x ^{3}} = \frac{6 x ^{5}}{x ^{3}} - \frac{3 x y ^{2}}{x ^{3}} + \frac{6}{x ^{3}}

= \frac{6 x ^{5}}{x ^{3}} - \frac{3 x y ^{2}}{x ^{3}} + \frac{6}{x ^{3}}

Cancel

\frac{6 x ^{5}}{x ^{3}} : 6 x^{2}

= 6 x^{2} - \frac{3 x y ^{2}}{x ^{3}} + \frac{6}{x ^{3}}

Cancel

\frac{3 x y ^{2}}{x ^{3}} : \frac{3 y ^{2}}{x ^{2}}

= 6 x^{2} - \frac{3 y ^{2}}{x ^{2}} + \frac{6}{x ^{3}}

(6 cos (2 x) + 3 sin (3 x) + c)^{2}

(x + x^{2} + y^{2}) d x + (y) d y

\frac{\partial}{\partial x} (x^{4}) + (x + 2 y + 2)^{4}

\frac{x y}{3} (3, 2, - 1)

(- 2 + \frac{31}{8}) 2

What is expand (3(2x^5-xy^2+2))/(x^3) ?
The solution to expand (3(2x^5-xy^2+2))/(x^3) is 6x^2-(3y^2)/(x^2)+6/(x^3)