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

A.

(\(\frac{5}{2}\), 1)

B.

(5, -4)

C.

(2, 1)

D.

(1, \(\frac{-5}{2}\))

E.

(1,-2)

Correct answer is D

\(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\)

\(\frac{2}{2r - 1}\) - \(\frac{1}{r + 2}\) = \(\frac{5}{3}\)

\(\frac{2r + 4 - 2r + 1}{2r - 1 (r + 2)}\) = \(\frac{5}{3}\)

\(\frac{5}{(2r + 1)(r + 2)}\) = \(\frac{5}{3}\)

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 \(\frac{-5}{2}\)