To simplify the expression \(\frac{2}{3xy} - \frac{3}{4yz}\), we need to find a common denominator and combine the two fractions.
The common denominator of the two fractions is 12xyz, which is the lowest multiple of 3xy and 4yz. We can convert each fraction to an equivalent fraction with the common denominator of 12xyz as follows:
2 3 4
-- - -- = --
3xy 4yz 12xyz
To find the numerators of the equivalent fractions, we multiply each numerator by the missing factor in the denominator of the other fraction. For example, we multiply the numerator of the first fraction by 4z to get a denominator of 12xyz, and we multiply the numerator of the second fraction by 3x to get a denominator of 12xyz:
2(4z) 3(3x) 8z - 9x
------ - ------ = --------
3xy(4z) 4yz(3x) 12xyz
Now we can simplify the expression by combining the two fractions:
8z - 9x
--------
12xyz
Therefore, the simplified expression is \(\frac{8z-9x}{12xyz}\), which corresponds to.
Therefore, the correct answer is: \(\frac{8z-9x}{12xyz}\).