Select the correct answer.

Find the quotient.

[tex]\[ \frac{2x - 3}{x} \div \frac{7}{x^2} \][/tex]

A. [tex]\(\frac{7}{x(2x - 3)}\)[/tex]

B. [tex]\(\frac{7x}{2x - 3}\)[/tex]

C. [tex]\(\frac{2x - 3}{7x}\)[/tex]

D. [tex]\(\frac{x(2x - 3)}{7}\)[/tex]



Answer :

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]