Simplify (xz-4z)/(z^2(4-x))

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

Factor $z$ out of $x z - 4 z$ .

Factor $z$ out of $x z$ .

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

Factor $z$ out of $- 4 z$ .

$\frac{z x + z \cdot - 4}{z^{2} (4 - x)}$

Factor $z$ out of $z x + z \cdot - 4$ .

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

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

Cancel the common factors.

Factor $z$ out of $z^{2} (4 - x)$ .

$\frac{z (x - 4)}{z (z (4 - x))}$

Cancel the common factor.

$\frac{z (x - 4)}{z (z (4 - x))}$

Rewrite the expression.

$\frac{x - 4}{z (4 - x)}$

$\frac{x - 4}{z (4 - x)}$

Cancel the common factor of $x - 4$ and $4 - x$ .

Factor $- 1$ out of $x$ .

$\frac{- 1 (- x) - 4}{z (4 - x)}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (- x) - 1 (4)}{z (4 - x)}$

Factor $- 1$ out of $- 1 (- x) - 1 (4)$ .

$\frac{- 1 (- x + 4)}{z (4 - x)}$

Reorder terms.

$\frac{- 1 (- x + 4)}{z (- x + 4)}$

Cancel the common factor.

$\frac{- 1 (- x + 4)}{z (- x + 4)}$

Rewrite the expression.

$\frac{- 1}{z}$

$\frac{- 1}{z}$

Move the negative in front of the fraction.

$- \frac{1}{z}$

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