Solve the following equation (frac{2}{2r – 1}) – (frac{5}{3}) = (frac{1}{r + 2})

Solve the following equation (frac{2}{2r – 1}) – (frac{5}{3}) = (frac{1}{r + 2})

Correct Answer: Option D

Explanation

(frac{2}{2r – 1}) – (frac{5}{3}) = (frac{1}{r + 2})
(frac{2}{2r – 1}) – (frac{1}{r + 2}) = (frac{5}{3})
(frac{2r + 4 – 2r + 1}{2r – 1 (r + 2)}) = (frac{5}{3})
(frac{5}{(2r + 1)(r + 2)}) = (frac{5}{3})
5(2r – 1)(r + 2) = 15
(10r – 5)(r + 2) = 15
10r² + 20r – 5r – 10 = 15
10r² + 15r = 25
10r² + 15r – 25 = 0
2r² + 3r – 5 = 0
(2r² + 5r)(2r + 5) = r(2r + 5) – 1(2r + 5)
(r – 1)(2r + 5) = 0
r = 1 or (frac{-5}{2})