1. **State the problem:** Simplify the expression $$y = \frac{\sin 2x}{\sin x}$$ and understand its behavior. 2. **Recall the double-angle formula for sine:** $$\sin 2x = 2 \sin x \cos x$$. 3. **Substitute the formula into the expression:** $$y = \frac{2 \sin x \cos x}{\sin x}$$ 4. **Simplify by canceling $$\sin x$$ (assuming $$\sin x \neq 0$$):** $$y = 2 \cos x$$ 5. **Interpretation:** The function simplifies to $$y = 2 \cos x$$, which is a cosine wave with amplitude 2. 6. **Important note:** The original function is undefined where $$\sin x = 0$$, i.e., at $$x = k\pi$$ for integers $$k$$, because division by zero is undefined. 7. **Summary:** The graph of $$y = \frac{\sin 2x}{\sin x}$$ matches the graph of $$y = 2 \cos x$$ except at points where $$\sin x = 0$$, where the function has vertical asymptotes or is undefined. **Final answer:** $$y = 2 \cos x$$ (for $$x \neq k\pi$$).