Solve x/x-5>1/2, when x ϵ R.

Answer :Observe that       is zero at x = -5 and not defined at x = 5 Hence plotting these two points on number line

Now for x > 5  is positive

For every root and not defined value of the sign will change

We want greater than zero that is the positive part hence x < -5 and x > 5

x < -5 means x is from negative infinity to -5 and x > 5 means x is from 5 to infinity Hence x ∈ (-∞, -5) U (5, ∞)

Hence solution is x ∈ (-∞, 2) U (5, ∞)