0 = (x - 1)/(x - 5) - (x + 2)/(x + 3)

Since the LCD is (x - 5)(x + 3), multiply that by both sides:

[0 = (x - 1)/(x - 5) - (x + 2)/(x + 3)](x - 5)(x + 3)
0 = (x - 1)(x + 3) - (x + 2)(x - 5)
0 = x² + 2x - 3 - (x² - 3x - 10)
0 = x² + 2x - 3 - x² + 3x + 10
0 = 5x + 7
5x = -7
x = -7/5

I hope this helps!

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