SOLUTION: 1/x-1 + 1/x+2 = 5/4 Find all real solutions of the equation

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1/(x - 1) + 1/(x + 2) = 5/4
(x - 1)/(x - 1) + (x - 1)/(x + 2) = 5(x - 1)/4
1 + (x - 1)/(x + 2) = 5(x - 1)/4
(x + 2) + (x - 1)(x + 2)/(x + 2) = 5(x - 1)(x + 2)/4
(x + 2) + (x - 1) = 5(x - 1)(x + 2)/4
4(x + 2) + 4(x - 1) = 5*4(x - 1)(x + 2)/4
4x + 8 + 4x - 4 = 5x^2 + 5x - 10
0 = 5x^2 - 3x - 14
0 = 5x^2 - 10x + 7x - 14
0 = (5x^2 - 10x) + (7x - 14)
0 = 5x(x - 2) + 7(x - 2)
0 = (5x + 7)(x - 2)
x = -7/5
x = 2