Question

$$\frac{6x - 3}{5x^2} \div \frac{5}{x}$$
\bigcirc a. \\(\frac{6x - 3}{25x}\\)
\bigcirc b. \\(\frac{25x}{6x - 3}\\)
\bigcirc c. \\(\frac{6x - 3}{25x^3}\\)
\bigcirc d. \\(\frac{25x^2}{2x - 3}\\)

Explanation:

Step1: Recall division of fractions

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, $\frac{6x - 3}{5x^2} \div \frac{5}{x}$ becomes $\frac{6x - 3}{5x^2} \times \frac{x}{5}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $(6x - 3) \times x = x(6x - 3)$. Multiply the denominators: $5x^2 \times 5 = 25x^2$. So we have $\frac{x(6x - 3)}{25x^2}$.

Step3: Simplify the fraction

We can cancel out one $x$ from the numerator and the denominator. So $\frac{x(6x - 3)}{25x^2}=\frac{6x - 3}{25x}$.

Answer:

A. $\frac{6x - 3}{25x}$