Question: Divide $\frac{32r + 4}{r} \div \frac{8r + 1}{r^3}$. $$\frac{32r + 4}{r} \div \frac{8r +…

Divide $\frac{32r + 4}{r} \div \frac{8r + 1}{r^3}$.

$$\frac{32r + 4}{r} \div \frac{8r + 1}{r^3} =$$

(Type your answer using exponential notation. Simplify your answer.)

Solution

To solve the problem, follow these steps: Start by rewriting the division as multiplication by the reciprocal: \[ \frac{32r + 4}{r} \times \frac{r^3}{8r + 1} \] Factor out the common term in the numerator: \[ \frac{4(8r + 1)}{r} \times \frac{r^3}{8r + 1} \] Cancel the common factors \((8r + 1)\): \[ \frac{4}{r} \times r^3 \] Simplify the expression by subtracting the exponents: \[ 4r^{2} \] Final Answer: \(4r^{2}\)