Simplify: (frac{5}{x – y} – frac{4}{y – x})
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A.
9x – y
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B.
9y – x
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C.
1x – y
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D.
1y – x
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E.
y – 9xx – y
Correct Answer: Option A
Explanation
(frac{5}{x – y} – frac{4}{y – x})
= (frac{5(y – x) – 4(x – y)}{(x – y)(y – x)})
= (frac{5y – 5x – 4x + 4y}{(x – y)(y – x)})
= (frac{9y – 9x}{(x – y)(y – x)})
= (frac{9(y – x)}{(x – y)(y – x)})
= (frac{9}{x – y})