Home » Past Questions » Mathematics » Simplify: \(\frac{3x - y}{xy} + \frac{2x + 3y}{2xy} + \frac{1}{2}\)

Simplify: \(\frac{3x - y}{xy} + \frac{2x + 3y}{2xy} + \frac{1}{2}\)


Question

Simplify: \(\frac{3x - y}{xy} + \frac{2x + 3y}{2xy} + \frac{1}{2}\)

Options

A) \(\frac{4x + 5y - xy}{2xy}\)

B) \(\frac{5y - 4x + xy}{2xy}\)

C) \(\frac{5x + 4y - xy}{2xy}\)

D) \(\frac{4x - 5y + xy}{2xy}\)

The correct answer is D.

Explanation:

\(\frac{3x - y}{xy} + \frac{2x + 3y}{2xy} + \frac{1}{2}\)

= \(\frac{2(3x - y) - 1(2x + 3y) + xy}{2xy}\)

= \(\frac{6x - 2y - 2x - 3y + xy}{2xy}\)

= \(\frac{4x - 5y + xy}{2xy}\)


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Dicussion (1)

  • \(\frac{3x - y}{xy} + \frac{2x + 3y}{2xy} + \frac{1}{2}\)

    = \(\frac{2(3x - y) - 1(2x + 3y) + xy}{2xy}\)

    = \(\frac{6x - 2y - 2x - 3y + xy}{2xy}\)

    = \(\frac{4x - 5y + xy}{2xy}\)

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