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

\(10r^2\) + 20r - 5r - 10 = 15

\(10r^2\) + 15r = 25

\(10r^2\) + 15r - 25 = 0

\(2r^2\) + 3r - 5 = 0

(\(2r^2 + 5r)\)(2r + 5) = r(2r + 5) - 1(2r + 5)

(r - 1)(2r + 5) = 0

r = 1 or \(\frac{-5}{2}\)

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