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

The solution to expand (-y^2+(x-2)^2)/(y^3) is -1/y+(x^2)/(y^3)-(4x)/(y^3)+4/(y^3)

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

expand

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

- \frac{1}{y} + \frac{x ^{2}}{y ^{3}} - \frac{4 x}{y ^{3}} + \frac{4}{y ^{3}}

Solution steps

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

Expand

- y^{2} + (x - 2)^{2} : - y^{2} + x^{2} - 4 x + 4

= \frac{- y ^{2} + x ^{2} - 4 x + 4}{y ^{3}}

Apply the fraction rule:

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

\frac{- y ^{2} + x ^{2} - 4 x + 4}{y ^{3}} = - \frac{y ^{2}}{y ^{3}} + \frac{x ^{2}}{y ^{3}} - \frac{4 x}{y ^{3}} + \frac{4}{y ^{3}}

= - \frac{y ^{2}}{y ^{3}} + \frac{x ^{2}}{y ^{3}} - \frac{4 x}{y ^{3}} + \frac{4}{y ^{3}}

Cancel

\frac{y ^{2}}{y ^{3}} : \frac{1}{y}

= - \frac{1}{y} + \frac{x ^{2}}{y ^{3}} - \frac{4 x}{y ^{3}} + \frac{4}{y ^{3}}

\frac{1}{( y - m ) ( y - n )}

- \frac{2 x ^{2} + 5 x + 9}{( x ^{2} + 7 ) ( x - 1 )}

\frac{1}{( 6 x + 5 ) ^{9}}

\frac{x ( x - 1 ) ( x - 2 )}{6}

(e - 5) (f - 2 g)

What is expand (-y^2+(x-2)^2)/(y^3) ?
The solution to expand (-y^2+(x-2)^2)/(y^3) is -1/y+(x^2)/(y^3)-(4x)/(y^3)+4/(y^3)