Reduce the fraction to lowest terms.
38x^2yz^2
_________=
-19xy^2z^3
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To reduce the given fraction to its lowest terms, we need to find the greatest common factor (GCF) of the numerator and denominator and divide both of them by it.
Let's break down the numerator and denominator into their prime factors:
Numerator: 38x^2yz^2
The prime factors of 38 are 2 and 19.
The prime factors of x^2 are x and x.
The prime factors of y are y.
The prime factors of z^2 are z and z.
So, the prime factorization of the numerator is 2 * 19 * x * x * y * z * z.
Denominator: -19xy^2z^3
Since there is a negative sign in front of the fraction, we will consider the numerator and denominator separately for finding prime factors.
The prime factors of 19 are 19.
The prime factors of x are x.
The prime factors of y^2 are y and y.
The prime factors of z^3 are z, z, and z.
So, the prime factorization of the denominator is -19 * x * y * y * z * z * z.
Now, let's cancel out the common factors between the numerator and denominator:
Numerator: 2 * x * y * z * z
Denominator: -1 * x * y * y * z * z * z
We can cancel out the factor of x, y, z, and z from both the numerator and the denominator.
After canceling out the common factors, we are left with:
Final Fraction: 2 * z
_______
-1 * y * z
Which simplifies to:
Final Fraction: -2z
_______
y
Therefore, the given fraction, when reduced to lowest terms, is -2z/y.