1. **State the problem:** Simplify the expression $$\frac{\sin x \cdot x^{2}}{|\theta x m x|} + \frac{\sin x}{|\theta x m x|^{2}}.$$\n\n2. **Identify the components:** The expression has two terms with denominators involving absolute values and powers.\n\n3. **Rewrite the expression:** Let $$A = |\theta x m x|.$$ Then the expression becomes $$\frac{\sin x \cdot x^{2}}{A} + \frac{\sin x}{A^{2}}.$$\n\n4. **Find a common denominator:** The common denominator is $$A^{2}.$$ Rewrite the first term: $$\frac{\sin x \cdot x^{2}}{A} = \frac{\sin x \cdot x^{2} \cdot A}{A^{2}}.$$\n\n5. **Combine the terms:** $$\frac{\sin x \cdot x^{2} \cdot A}{A^{2}} + \frac{\sin x}{A^{2}} = \frac{\sin x (x^{2} A + 1)}{A^{2}}.$$\n\n6. **Final simplified form:** $$\boxed{\frac{\sin x (x^{2} |\theta x m x| + 1)}{|\theta x m x|^{2}}}.$$\n\nThis is the simplified expression in terms of the original variables.