What is (9x^6y^3-6x^4y^2-3x^2y^5)/(3x^2y) ?

The solution to (9x^6y^3-6x^4y^2-3x^2y^5)/(3x^2y) is y(3x^4y-2x^2-y^3)

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simplify (9x^6y^3-6x^4y^2-3x^2y^5)/(3x^2y)

simplify

\frac{9 x ^{6} y ^{3} - 6 x ^{4} y ^{2} - 3 x ^{2} y ^{5}}{3 x ^{2} y}

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

Solution steps

\frac{9 x ^{6} y ^{3} - 6 x ^{4} y ^{2} - 3 x ^{2} y ^{5}}{3 x ^{2} y}

Factor

9 x^{6} y^{3} - 6 x^{4} y^{2} - 3 x^{2} y^{5} : 3 x^{2} y^{2} (3 x^{4} y - 2 x^{2} - y^{3})

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

Cancel the common factor:

3

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

Cancel the common factor:

x^{2}

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

Apply exponent rule:

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

y^{2} = yy

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

Cancel the common factor:

y

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

7 \frac{3}{4}

\frac{7}{3} - \frac{8}{12 x - 8}

\frac{21 x ^{7} y ^{5}}{35 x ^{3} y ^{2}}

x (x + 1)^{2}

What is (9x^6y^3-6x^4y^2-3x^2y^5)/(3x^2y) ?
The solution to (9x^6y^3-6x^4y^2-3x^2y^5)/(3x^2y) is y(3x^4y-2x^2-y^3)