What is expand (-3(x+y)^2+2(x+y)+1)/y ?

The solution to expand (-3(x+y)^2+2(x+y)+1)/y is -(3x^2)/y-6x-3y+(2x)/y+2+1/y

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expand (-3(x+y)^2+2(x+y)+1)/y

expand

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

- \frac{3 x ^{2}}{y} - 6 x - 3 y + \frac{2 x}{y} + 2 + \frac{1}{y}

Solution steps

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

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

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

Expand

- 3 (x^{2} + 2 x y + y^{2}) + 2 (x + y) + 1 : - 3 x^{2} - 6 x y - 3 y^{2} + 2 x + 2 y + 1

= \frac{- 3 x ^{2} - 6 x y - 3 y ^{2} + 2 x + 2 y + 1}{y}

Apply the fraction rule:

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

\frac{- 3 x ^{2} - 6 x y - 3 y ^{2} + 2 x + 2 y + 1}{y} = - \frac{3 x ^{2}}{y} - \frac{6 x y}{y} - \frac{3 y ^{2}}{y} + \frac{2 x}{y} + \frac{2 y}{y} + \frac{1}{y}

= - \frac{3 x ^{2}}{y} - \frac{6 x y}{y} - \frac{3 y ^{2}}{y} + \frac{2 x}{y} + \frac{2 y}{y} + \frac{1}{y}

Cancel

\frac{6 x y}{y} : 6 x

= - \frac{3 x ^{2}}{y} - 6 x - \frac{3 y ^{2}}{y} + \frac{2 x}{y} + \frac{2 y}{y} + \frac{1}{y}

Cancel

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

= - \frac{3 x ^{2}}{y} - 6 x - 3 y + \frac{2 x}{y} + \frac{2 y}{y} + \frac{1}{y}

Cancel

\frac{2 y}{y} : 2

= - \frac{3 x ^{2}}{y} - 6 x - 3 y + \frac{2 x}{y} + 2 + \frac{1}{y}

g (- 2 = 5 - (2)^{2})

(x - 3 y + 2) d x + 3 (x + 3 y - 4) d y

y (I n y -, - 1) d x

3 \cdot 3 \frac{3}{4}

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

What is expand (-3(x+y)^2+2(x+y)+1)/y ?
The solution to expand (-3(x+y)^2+2(x+y)+1)/y is -(3x^2)/y-6x-3y+(2x)/y+2+1/y