1. **State the problem:** Simplify the expression $$\frac{96h^{5}r^{18} + 36h^{10}r^{12} - 120h^{45}r^{3}}{12h^{5}r^{3}}$$ where $h \neq 0$ and $r \neq 0$. 2. **Write the expression as separate fractions:** $$\frac{96h^{5}r^{18}}{12h^{5}r^{3}} + \frac{36h^{10}r^{12}}{12h^{5}r^{3}} - \frac{120h^{45}r^{3}}{12h^{5}r^{3}}$$ 3. **Simplify each term by dividing coefficients and subtracting exponents of like bases:** - First term: $$\frac{96}{12} \cdot \frac{h^{5}}{h^{5}} \cdot \frac{r^{18}}{r^{3}} = 8 \cdot \cancel{1} \cdot r^{18-3} = 8r^{15}$$ - Second term: $$\frac{36}{12} \cdot \frac{h^{10}}{h^{5}} \cdot \frac{r^{12}}{r^{3}} = 3 \cdot h^{10-5} \cdot r^{12-3} = 3h^{5}r^{9}$$ - Third term: $$\frac{120}{12} \cdot \frac{h^{45}}{h^{5}} \cdot \frac{r^{3}}{r^{3}} = 10 \cdot h^{45-5} \cdot \cancel{1} = 10h^{40}$$ 4. **Combine the simplified terms:** $$8r^{15} + 3h^{5}r^{9} - 10h^{40}$$ 5. **Answer:** An equivalent expression of the given expression is $8r^{15} + 3h^{5}r^{9} - 10h^{40}$. **Note:** The order of terms can be rearranged, but the coefficients and powers must match.