# How do you simplify (2xyz)/(x^2z^2)div (6y^3)/(3xz)?

Mar 2, 2017

$\setminus \frac{1}{{y}^{2}}$

#### Explanation:

When we divide one fraction with another one, we can rewrite it as multiplication of first fraction by the second one, it means:
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \setminus \times \frac{d}{c} = \frac{a d}{b c}$

so let's do the trick and see what'll happen
$\setminus \frac{2 x y z}{{x}^{2} {z}^{2}} \div \setminus \frac{6 {y}^{3}}{3 x z} = \setminus \frac{2 x y z}{{x}^{2} {z}^{2}} \setminus \times \setminus \frac{3 x z}{6 {y}^{3}}$

and we simply multiply the numerator by the numerator and the denominator by the denominator.
$\setminus \frac{2 x y z}{{x}^{2} {z}^{2}} \setminus \times \setminus \frac{3 x z}{6 {y}^{3}} = \setminus \frac{6 {x}^{2} y {z}^{2}}{6 {x}^{2} {y}^{3} {z}^{2}}$
and by simplifying this fraction we get:

$\setminus \frac{6 {x}^{2} y {z}^{2}}{6 {x}^{2} {y}^{3} {z}^{2}} = \setminus \frac{1}{{y}^{2}}$