Simplify (-5x^2y^3z^4)/(15x^4y^2z^4)

$\frac{- 5 x^{2} y^{3} z^{4}}{15 x^{4} y^{2} z^{4}}$

Step 1

Cancel the common factor of $- 5$ and $15$ .

Factor $5$ out of $- 5 x^{2} y^{3} z^{4}$ .

$\frac{5 (- x^{2} y^{3} z^{4})}{15 x^{4} y^{2} z^{4}}$

Cancel the common factors.

Factor $5$ out of $15 x^{4} y^{2} z^{4}$ .

$\frac{5 (- x^{2} y^{3} z^{4})}{5 (3 x^{4} y^{2} z^{4})}$

Cancel the common factor.

$\frac{5 (- x^{2} y^{3} z^{4})}{5 (3 x^{4} y^{2} z^{4})}$

Rewrite the expression.

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

Step 2

Cancel the common factor of $x^{2}$ and $x^{4}$ .

Factor $x^{2}$ out of $- x^{2} y^{3} z^{4}$ .

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

Cancel the common factors.

Factor $x^{2}$ out of $3 x^{4} y^{2} z^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1 y^{3} z^{4}}{3 x^{2} y^{2} z^{4}}$

Step 3

Cancel the common factor of $y^{3}$ and $y^{2}$ .

Factor $y^{2}$ out of $- 1 y^{3} z^{4}$ .

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

Cancel the common factors.

Factor $y^{2}$ out of $3 x^{2} y^{2} z^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1 y z^{4}}{3 x^{2} z^{4}}$

Step 4

Cancel the common factor of $z^{4}$ .

Cancel the common factor.

$\frac{- 1 y z^{4}}{3 x^{2} z^{4}}$

Rewrite the expression.

$\frac{- 1 y}{3 x^{2}}$

Step 5

Move the negative in front of the fraction.

$- \frac{y}{3 x^{2}}$