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]
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]
