What is expand (10x^2y^2-8xy^3+6y)/(2y^2) ?

The solution to expand (10x^2y^2-8xy^3+6y)/(2y^2) is 5x^2-4xy+3/y

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expand (10x^2y^2-8xy^3+6y)/(2y^2)

expand

\frac{10 x ^{2} y ^{2} - 8 x y ^{3} + 6 y}{2 y ^{2}}

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

Solution steps

\frac{10 x ^{2} y ^{2} - 8 x y ^{3} + 6 y}{2 y ^{2}}

Factor

10 x^{2} y^{2} - 8 x y^{3} + 6 y : 2 y (5 x^{2} y - 4 x y^{2} + 3)

= \frac{2 y ( 5 x ^{2} y - 4 x y ^{2} + 3 )}{2 y ^{2}}

Cancel

\frac{2 y ( 5 x ^{2} y - 4 x y ^{2} + 3 )}{2 y ^{2}} : \frac{5 x ^{2} y - 4 x y ^{2} + 3}{y}

= \frac{5 x ^{2} y - 4 x y ^{2} + 3}{y}

Apply the fraction rule:

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

\frac{5 x ^{2} y - 4 x y ^{2} + 3}{y} = \frac{5 x ^{2} y}{y} - \frac{4 x y ^{2}}{y} + \frac{3}{y}

= \frac{5 x ^{2} y}{y} - \frac{4 x y ^{2}}{y} + \frac{3}{y}

Cancel

\frac{5 x ^{2} y}{y} : 5 x^{2}

= 5 x^{2} - \frac{4 x y ^{2}}{y} + \frac{3}{y}

Cancel

\frac{4 x y ^{2}}{y} : 4 x y

= 5 x^{2} - 4 x y + \frac{3}{y}

\frac{1}{x ^{2} ( t x - 1 )}

sin^{2} (x) (cot (x) + 1)^{2}

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

- (\frac{2 ( 2 s + 11 )}{( s ( s + 5 ) )})

- \frac{5 ( x + 4 )}{2 ( x + 3 )}

What is expand (10x^2y^2-8xy^3+6y)/(2y^2) ?
The solution to expand (10x^2y^2-8xy^3+6y)/(2y^2) is 5x^2-4xy+3/y