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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

\frac{y}{y ^{2}} : \frac{1}{y}

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

(8 y + 3 e) (5 y + 4 e)

e^{t (1 + i)}

\frac{f ( x - 3 )}{2}

7 (51 - 4 p = 16)

\frac{13 x ( 2 x + 1 )}{2}

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