Solve the following equation frac 2 2r - 1 - fr... - JAMB Mathematics 2021 Question

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

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

L.C.M. => (2r - 1) (r + 2) 

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

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

3 = (2r - 1) (r + 2) or 2r\(^2\) + 3r - 2 

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

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

x = 1 or - \(\frac{5}{2}\)