Simplify: 3x - y/xy - 2x + 3y/2xy + 1/2

Correct Answer is : 4x−5y+xy2xy4x - 5y + xy/2xy2xy4x−5y+xy

Correct Answer is : 4x−5y+xy2xy4x - 5y + xy/2xy2xy4x−5y+xy

Test Index

WAEC Mathematics 2015 Paper

Question : 34

Total: 45

Simplify:

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

Solution:

Concept:

To simplify algebraic fractions, rewrite every term over one common denominator.

Explanation:

The least common denominator of

xy

2xy

, and

2

2xy

Write each fraction with denominator

2xy

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

\frac{2x+3y}{2xy}

remains unchanged.

\frac{1}{2} = \frac{xy}{2xy}

Now combine the numerators:

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

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

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

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

This matches option D.

Answer:

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

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