Answer:
x = 1/2 [ 1 - √61] , 1/2 [1 + √61].
Step-by-step explanation:
3 /( x^2 - 2x - 8) - 1 / (x + 2) = 1
3 / ( x - 4)(x + 2) - 1 / (x + 2) = 1
Multiply through by the LCD (x - 4)(x + 2):
3 - 1(x - 4) = (x - 4)(x + 2)
3 - x + 4 = x^2 - 2x - 8
x^2 - x - 15 = 0
x = [(-(-1) +/- sqrt (1 - 4* -15) / 2]
x = 1/2 [ 1 - √61] , 1/2 [1 + √61].
