Mathematics

Simplify: (frac{5}{x – y} – frac{4}{y – x})

Simplify: (frac{5}{x – y} – frac{4}{y – x})

  • A.

    9/x – y
  • B.

    9/y – x
  • C.

    1/x – y
  • D.

    1/y – x
  • E.

    y – 9x/x – 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})