Select the correct answer. Find the quotient. \( \frac{2 x-3}{x} \div \frac{7}{a^{2}} \) A. \( \frac{7}{2(2 x-3)} \) B. \( \frac{7 x}{2 x-3} \) C. \( \frac{2 x-3}{7 x} \) D. \( \frac{x(2 x-3)}{7} \) Next

To solve the expression \( \frac{2 x-3}{x} \div \frac{7}{a^{2}} \), we first rewrite the division as multiplication by the reciprocal: \( \frac{2 x-3}{x} \times \frac{a^2}{7} \). Now we can simplify this expression: 1. Combine the products: \( \frac{(2 x-3) \cdot a^2}{7 x} \). 2. This cannot be simplified further without additional information about \( a \) or the value of \( x \). None of the answer choices directly match this expanded form, so let's double check any values or assumptions. The correct answer is **not listed** among the options given if we strictly adhere to the mathematical simplification process! Now for a little extra nugget of wisdom and fun facts! Did you know that long division isn't just for numbers? This technique can also be applied to polynomials! Understanding how to manipulate expressions can unlock more advanced math concepts down the road, making it a handy skill for tackling algebraic challenges head-on! Speaking of tackling challenges, one common pitfall in algebra is forgetting to apply the "multiply by the reciprocal" rule when dividing fractions. Always double-check that step! It’s the kind of mistake that can lead to some seriously tangled equations, or worse, completely incorrect final answers!