Given:

.

Signs of x – 7:

x – 7 = 0 → x = 7(Adding 7 on both the sides)

x – 7 > 0 → x > 7 (Adding 7 on both the sides)

x – 7 < 0 → x < 7 (Adding 7 on both the sides)

Signs of x – 2:

x – 2 = 0 → x = 2 (Adding 2 on both the sides)

x – 2 > 0 → x > 2 (Adding 2 on both the sides)

x – 2 < 0 → x < 2 (Adding 2 on both the sides)

Zeroes of denominator:

x – 2 = 0 → at x = 2 will be undefined.

Intervals that satisfy the required condition: ≥ 0

x < 2 or x = 7 or x >7

Therefore,

x є (-∞, -2) υ [7, ∞)