1. **State the problem:** Simplify the expression $$\frac{\sqrt{c+h}-\sqrt{c}}{h}$$ where $h \neq 0$. 2. **Recall the formula:** To simplify expressions involving differences of square roots, multiply numerator and denominator by the conjugate of the numerator. 3. **Multiply by the conjugate:** Multiply numerator and denominator by $$\sqrt{c+h}+\sqrt{c}$$: $$\frac{\sqrt{c+h}-\sqrt{c}}{h} \times \frac{\sqrt{c+h}+\sqrt{c}}{\sqrt{c+h}+\sqrt{c}} = \frac{(\sqrt{c+h}-\sqrt{c})(\sqrt{c+h}+\sqrt{c})}{h(\sqrt{c+h}+\sqrt{c})}$$ 4. **Use difference of squares:** The numerator becomes: $$ (\sqrt{c+h})^2 - (\sqrt{c})^2 = (c+h) - c = h $$ 5. **Substitute back:** $$\frac{h}{h(\sqrt{c+h}+\sqrt{c})}$$ 6. **Cancel common factor $h$:** $$\frac{\cancel{h}}{\cancel{h}(\sqrt{c+h}+\sqrt{c})} = \frac{1}{\sqrt{c+h}+\sqrt{c}}$$ 7. **Final simplified form:** $$\boxed{\frac{1}{\sqrt{c+h}+\sqrt{c}}}$$ This is the simplified form of the original expression, valid for $h \neq 0$ and $c+h \geq 0$, $c \geq 0$ to keep the square roots defined.