Solve x + 3/ x − 1 > 0, x ∈ R.

Question

Solve \(\frac{x+3}{x-1}\)> 0, x ∈ R.

Answer 1

We have, 

\(\frac{x+3}{x-1}\) > .... (i)

Equation x-1 and x + 3 to zero, we obtain x = 1, -3 as critical points. Plot these points on real line as shown in figure. The real line is divided into three regions. In the right most region the expression on LHS of (i) is positive and in the remaining two regions it is alternatively negative

 

And positive. Since the expression in (i) is positive, so the solution set is given by

\(\frac{x+3}{x-1}\) > 0

⇒ (−∞, −3) ∪ (1, ∞)