1. **State the problem:** Solve the equation $\frac{X \cdot x + x}{x} = 10$ for $X$. 2. **Rewrite the expression:** The numerator is $X \cdot x + x$, and the denominator is $x$. We can factor $x$ out of the numerator: $$\frac{x(X + 1)}{x} = 10$$ 3. **Simplify the fraction:** Since $x \neq 0$, we can cancel $x$ in numerator and denominator: $$\frac{\cancel{x}(X + 1)}{\cancel{x}} = 10$$ which simplifies to $$X + 1 = 10$$ 4. **Solve for $X$:** Subtract 1 from both sides: $$X + 1 - 1 = 10 - 1$$ $$X = 9$$ **Final answer:** $X = 9$