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

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

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simplify y^2(x/(y^3)-3)

simplify

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

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

Solution steps

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

Join

\frac{x}{y ^{3}} - 3 : \frac{- 3 y ^{3} + x}{y ^{3}}

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

Apply the fraction rule:

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

y^{3} = y^{2} y

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

Cancel the common factor:

y^{2}

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

\frac{x ^{2} + 2 x - 18}{( x + 4 ) x ^{3}}

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

(x + a) (x + b) - x

\frac{1}{( s - 2 ) ( s ^{2} - 2 s + 1 )}

(t sin (t)) \cdot (sin (t) + t cos (t))