1. **State the problem:** Simplify the expression $a(\sinh(\frac{b}{a}) - \sinh(-\frac{b}{a}))$. 2. **Recall the property of hyperbolic sine:** $\sinh(-x) = -\sinh(x)$. 3. **Apply the property:** $$\sinh(-\frac{b}{a}) = -\sinh(\frac{b}{a})$$ 4. **Substitute back into the expression:** $$a\left(\sinh\left(\frac{b}{a}\right) - (-\sinh\left(\frac{b}{a}\right))\right) = a\left(\sinh\left(\frac{b}{a}\right) + \sinh\left(\frac{b}{a}\right)\right)$$ 5. **Combine like terms:** $$a \times 2 \sinh\left(\frac{b}{a}\right) = 2a \sinh\left(\frac{b}{a}\right)$$ **Final answer:** $$2a \sinh\left(\frac{b}{a}\right)$$