Clearly in this question we need to see all the values in which denominator is not 0 and the value inside the root is not negative.

Hence, x^2 - 7x - 8 > 0

x^2 - 8x + x - 8 > 0

x ( x - 8 ) + 1 ( x - 8 ) > 0

( x + 1 ) ( x - 8 ) > 0

Hence, the required subset becomes.

( - infinite , -1 ) and ( 8 , infinity )

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