To find the product of the fractions [tex]\(\frac{x}{3}\)[/tex] and [tex]\(\frac{6}{x}\)[/tex] when [tex]\(x \neq 0\)[/tex], we proceed with the following steps:
1. Write down the given fractions:
[tex]\[
\text{First fraction: } \frac{x}{3}
\][/tex]
[tex]\[
\text{Second fraction: } \frac{6}{x}
\][/tex]
2. Multiply the fractions:
To find the product of two fractions, we multiply the numerators together and the denominators together.
[tex]\[
\frac{x}{3} \times \frac{6}{x} = \frac{x \cdot 6}{3 \cdot x}
\][/tex]
3. Simplify the expression:
To simplify, observe that [tex]\(x\)[/tex] in the numerator and denominator can cancel each other out, as long as [tex]\(x \neq 0\)[/tex]:
[tex]\[
\frac{x \cdot 6}{3 \cdot x} = \frac{6}{3}
\][/tex]
4. Further simplify the resulting fraction:
[tex]\[
\frac{6}{3} = 2
\][/tex]
Therefore, the product of the fractions [tex]\(\frac{x}{3}\)[/tex] and [tex]\(\frac{6}{x}\)[/tex] is [tex]\(2\)[/tex].
The correct answer is:
2
