Option C:
The product of the expression is [tex]\frac{3 x^{2}}{x^{2}+x-2}[/tex].
Solution:
Given expression:
[tex]$\frac{3 x}{x+2} \cdot \frac{x}{x-1}[/tex]
To find the product of the expression:
[tex]$\frac{3 x}{x+2} \cdot \frac{x}{x-1}=\frac{3 x \cdot x}{(x+2)(x-1)}[/tex]
Multiply each term of first expression with each term of second expression.
[tex]$=\frac{3 x^2}{x^2-x+2x-2}[/tex]
[tex]$=\frac{3 x^2}{x^2+x-2}[/tex]
[tex]$\frac{3 x}{x+2} \cdot \frac{x}{x-1}=\frac{3 x^2}{x^2+x-2}[/tex]
Option C is the correct answer.
The product of the expression is [tex]\frac{3 x^{2}}{x^{2}+x-2}[/tex].
