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Simplify (frac{x + 2}{x + 1}) – (frac{x – 2}{x + 2})

Simplify (frac{x + 2}{x + 1}) – (frac{x – 2}{x + 2})
  • A.
    (frac{3}{x + 1})
  • B.
    (frac{3x + 2}{(x + 1)(x + 2)})
  • C.
    (frac{5x + 6}{(x + 1)(x + 2)})
  • D.
    (frac{2x^2 + 5x + 2}{(x + 1)(x + 2)})
Correct Answer: Option C
Explanation

(frac{x + 2}{x + 1}) – (frac{x – 2}{x + 2}) = (frac{(x + 2)(x + 2) – (x -2) – (x – 2)(x + 1)}{(x + 1)(x + 2)})
= (frac{(x^2 + 4x + 4) – (x^2 – x – 2)}{(x + 1)(x + 2)}) = (frac{x^2 + 4x + 4 – x^2 + x + 2}{(x + 1)(x + 2)})
= (frac{5x + 6}{(x + 1)(x + 2)})