Algebra Problem (Help Please)

Find the solutions of the equation: 1/x + 1/2 = 6/(x − 1) − 4/x.
A: x = 1; x = 5
B: x = -5; x = 2
C: x = -1; x = 0
D: x = -2; x = 5
E: x = −2; x = 3

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Hi!

1/x + 1/2 = 6/(x-1) - 4/x
(x-1)/x + (x-1)/2 = 6 - (4x+4)/x
x-1 + (x²-x)/2 = 6x -4x+4
2x-2 + x²-x = 12x -8x+8
x² - 3x - 10 = 0

Delta = b²-4ac = 49

x1 = (3-7)/2 = -2
x2 = (3+7)/2 = 5

Hope this helps!