What is ((x^2y^4-2xy^3+4y^2))/((3/2 y^2)) ?

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

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simplify ((x^2y^4-2xy^3+4y^2))/((3/2 y^2))

simplify

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

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

Solution steps

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

Factor

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

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

Cancel the common factor:

y^{2}

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

Apply the fraction rule:

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

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

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

(- 6 x y^{4})^{3}

5 (2)^{4}

1 + \frac{1 - 8 x}{x ^{2} + 4 x + 3} \leq 0

15 x^{3} - 9 x^{2} - 6 x

∣ 3 x - 2 ∣ \geq 7

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