If [tex]$\frac{2 y}{x} - \frac{y}{2 x} = \frac{\square}{2 x}$[/tex] and [tex]$x \neq 0$[/tex], what expression is represented by [tex]$\square$[/tex]?

A. [tex]$y$[/tex]
B. [tex]$2 y$[/tex]
C. [tex]$3 y$[/tex]
D. [tex]$4 y$[/tex]



Answer :

To find the expression represented by the box ([tex]$\square$[/tex]) in the equation [tex]\(\frac{2y}{x} - \frac{y}{2x} = \frac{\square}{2x}\)[/tex], follow these steps:

1. Combine the fractions on the left-hand side:
[tex]\[ \frac{2y}{x} - \frac{y}{2x} \][/tex]

2. Find a common denominator:
[tex]\[ \frac{2y}{x} = \frac{2y \cdot 2}{x \cdot 2} = \frac{4y}{2x} \][/tex]

So the equation now is:
[tex]\[ \frac{4y}{2x} - \frac{y}{2x} \][/tex]

3. Combine the fractions:
Since the denominators are the same, you can subtract the numerators:
[tex]\[ \frac{4y - y}{2x} = \frac{3y}{2x} \][/tex]

4. Equate the fractions:
Now compare the left-hand side with the right-hand side of the original equation:
[tex]\[ \frac{3y}{2x} = \frac{\square}{2x} \][/tex]

5. Solve for the expression:
Since the denominators are equal, the numerators must also be equal:
[tex]\[ 3y = \square \][/tex]

Thus, the expression represented by [tex]\(\square\)[/tex] is:

[tex]\[ \boxed{3y} \][/tex]

Therefore, the correct choice is [tex]\(G.\)[/tex]