What is (x^4y^5z-x^3y^4z^2+x^2y^4z)/(x^2y^3) ?

The solution to (x^4y^5z-x^3y^4z^2+x^2y^4z)/(x^2y^3) is yz(x^2y-xz+1)

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simplify (x^4y^5z-x^3y^4z^2+x^2y^4z)/(x^2y^3)

simplify

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

yz (x^{2} y - x z + 1)

Solution steps

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

Factor out common term

x^{2} y^{4} z : x^{2} y^{4} z (x^{2} y - x z + 1)

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

Cancel the common factor:

x^{2}

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

Apply exponent rule:

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

y^{4} = y^{3} y

= \frac{y ^{3} yz ( x ^{2} y - x z + 1 )}{y ^{3}}

Cancel the common factor:

y^{3}

= yz (x^{2} y - x z + 1)

\frac{( 12 u \cdot 10 v w )}{( 6 v \cdot 45 u )}

\frac{c}{d} + 1

\frac{2}{6} - \frac{2}{7}

y^{2} - 10 y + 24

\frac{48}{72}

What is (x^4y^5z-x^3y^4z^2+x^2y^4z)/(x^2y^3) ?
The solution to (x^4y^5z-x^3y^4z^2+x^2y^4z)/(x^2y^3) is yz(x^2y-xz+1)