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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

(e^{2 t} + 1)^{2}

cos (t) u (t - π)

x^{2} \cdot (50 + \frac{3 x}{2}) - 1000 x

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

(y^{3}) d x + (3 y^{2} + 3 x y^{2} - y^{3}) d y

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