What is expand ((x^3+y^2x-y)n)/y ?

The solution to expand ((x^3+y^2x-y)n)/y is (nx^3)/y+nxy-n

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expand ((x^3+y^2x-y)n)/y

expand

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

\frac{n x ^{3}}{y} + n x y - n

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

= \frac{n x ^{3}}{y} + n x y - \frac{n y}{y}

Cancel

\frac{n y}{y} : n

= \frac{n x ^{3}}{y} + n x y - n

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What is expand ((x^3+y^2x-y)n)/y ?
The solution to expand ((x^3+y^2x-y)n)/y is (nx^3)/y+nxy-n