Simplify: \(\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2}\)
A
\(\frac{4x + 5y - xy}{2xy}\)
B
\(\frac{5y - 4x + xy}{2xy}\)
C
\(\frac{5x + 4y - xy}{2xy}\)
D
\(\frac{4x - 5y + xy}{2xy}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2}\)
= \(\frac{2(3x - y) - 1(2x + 3y) + xy}{2xy}\)
= \(\frac{6x - 2y - 2x - 3y + xy}{2xy}\)
= \(\frac{4x - 5y + xy}{2xy}\)
Source: Myschool Past Questions Archive (Record #45906)