Observe that \(\frac{5-x}{x - 2}\) is zero at x = 5 and not defined at x = 2
Hence plotting these two points on number line
Now for x > 5, \(\frac{5-x}{x - 2}\) is negative
for every root and not defined value of \(\frac{5-x}{x - 2}\) the sign will change
We want the negative part hence x < 2 and x > 5
x < 2 means x is from negative infinity to 2 and x > 5 means x is from 5 to infinity
Hence x ∈ (-∞, 2) U (5, ∞)
Hence solution of \(\frac{3}{x-2}\) is x ∈ (-∞, 2) U (5, ∞)
