To find the quotient of the given expressions [tex]\(\frac{2x - 3}{x} \div \frac{7}{x^2}\)[/tex], follow these steps:
1. Write the division as a multiplication: When dividing by a fraction, multiply by its reciprocal.
[tex]\[
\frac{2x - 3}{x} \div \frac{7}{x^2} = \frac{2x - 3}{x} \cdot \frac{x^2}{7}
\][/tex]
2. Multiply the numerators and the denominators:
[tex]\[
\frac{(2x - 3) \cdot x^2}{x \cdot 7}
\][/tex]
3. Simplify the expression:
[tex]\[
\frac{(2x - 3) \cdot x^2}{7x} = \frac{x^2 (2x - 3)}{7x}
\][/tex]
We can simplify [tex]\(\frac{x^2}{x}\)[/tex] to [tex]\(x\)[/tex] (since [tex]\(x^2 / x = x\)[/tex]):
[tex]\[
\frac{x \cdot (2x - 3)}{7} = \frac{x(2x - 3)}{7}
\][/tex]
After simplifying, the result is:
[tex]\[
\frac{x(2x - 3)}{7}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{D. \frac{x(2x - 3)}{7}}
\][/tex]
