Subtract. \[ \frac{3}{5 u^{3} x^{2}}-\frac{7}{2 u^{2} x} \] Simplify your answer as much as possible.

To subtract the two fractions, we first need to find a common denominator. The denominators are \(5u^3x^2\) and \(2u^2x\). The least common multiple (LCM) of these denominators is \(10u^3x^2\). Next, we rewrite each fraction with the common denominator: 1. The first fraction: \[ \frac{3}{5u^{3}x^{2}} = \frac{3 \cdot 2}{5 \cdot 2 \cdot u^{3} \cdot x^{2}} = \frac{6}{10u^{3}x^{2}} \] 2. The second fraction: \[ \frac{7}{2u^{2}x} = \frac{7 \cdot 5u}{2 \cdot 5u \cdot u^{2} \cdot x^{2}} = \frac{35u}{10u^{3}x^{2}} \] Now we can subtract the two fractions: \[ \frac{6}{10u^{3}x^{2}} - \frac{35u}{10u^{3}x^{2}} = \frac{6 - 35u}{10u^{3}x^{2}} \] Thus, the simplified result is: \[ \frac{6 - 35u}{10u^{3}x^{2}} \]