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

Question

Savannah Anderson · Accepted Answer

#\frac{1}{y^2}# When we divide one fraction with another one, we can rewrite it as multiplication of first fraction by the second one, it means: #a/b -: c/d = a/b imes d/c = (ad)/(bc)# so let's do the trick and see what'll happen # \frac{2xyz}{x^2z^2} -: \frac{6y^3}{3xz} = \frac{2xyz}{x^2z^2} imes \frac{3xz}{6y^3}# and we simply multiply the numerator by the numerator and the denominator by the denominator. # \frac{2xyz}{x^2z^2} imes \frac{3xz}{6y^3} = \frac{6x^2yz^2}{6x^2y^3z^2}# and by simplifying this fraction we get: #\frac{6x^2yz^2}{6x^2y^3z^2} = \frac{1}{y^2}#

Jameson Allen · Answer

undefined To simplify the expression (2xyz)/(x^2z^2) ÷ (6y^3)/(3xz), we can follow these steps:

1. Invert the second fraction and change the division sign to multiplication: (2xyz)/(x^2z^2) × (3xz)/(6y^3)
2. Simplify the numerator: 2xyz × 3xz = 6x^2y^2z^2
3. Simplify the denominator: x^2z^2 × 6y^3 = 6x^2y^3z^2
4. Divide the simplified numerator by the simplified denominator: (6x^2y^2z^2) / (6x^2y^3z^2)
5. Cancel out common factors: The 6, x^2, and z^2 terms cancel out, leaving us with 1/y.

Therefore, the simplified expression is 1/y.