Question on: SS2 Mathematics - Algebraic Fractions
Simplify \(\frac{\frac{1}{2x} - \frac{4}{y}}{\frac{1}{x} + \frac{2}{3y}}\)
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A
\(\frac{2(8y - x)}{6(y + x)}\)
B
\(\frac{3(y - 8x)}{3(3y + 2x)}\)
C
\(\frac{2(2y - 8x)}{2(8y + 2x)}\)
D
\(\frac{3(y - 8x)}{2(3y + 2x)}\)
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Correct Option: D
\(Given\) \(\frac{\frac{1}{2x} - \frac{4}{y}}{\frac{1}{x} + \frac{2}{3y}}\)
\(Numerator\): \(\frac{1}{2x} - \frac{4}{y} = \ \frac{y - 8x}{2xy}\)
\(Denominator\): \(\frac{1}{x} + \frac{2}{3y} = \ \frac{3y + 2x}{3xy}\)
\(\frac{\frac{1}{2x} - \frac{4}{y}}{\frac{1}{x} + \frac{2}{3y}} = \ \frac{\frac{y - 8x}{2xy}}{\frac{3y + 2x}{3xy}} = \ \frac{y - 8x}{2xy} \div \frac{3y + 2x}{3xy} = \frac{y - 8x}{2xy} \times \frac{3xy}{3y + 2x} = \ \frac{y - 8x}{2} \times \frac{3}{3y + 2x} = \frac{3(y - 8x)}{2(3y + 2x)}\)
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