((x-1))/(x^2-4)>0 — step-by-step solution

1) Let's solve in

ℝ

\frac{x - 1}{x^{2} - 4} > 0

We study the sign of the numerator

⇥The expression

x - 1

is zero at

x = 1

, it is negative before and positive after

We study the sign of the denominator, which must not be zero

Let's study the sign of

x^{2} - 4

by solving in

ℝ

x^{2} - 4 > 0

An even power only depends on the absolute value:

x^{2} > 4

is equivalent to

| x | > 2

| A | > B

means that:

A > B

A < - B

2) Let's draw up the sign table:

Candidates, pending the domain check:

x \in (-2, 1) \cup (2, +∞)

3) Let's find the domain of

\frac{x - 1}{x^{2} - 4} > 0

For the expression

\frac{x - 1}{x^{2} - 4}

to be defined, we must have:

x^{2} - 4 \neq 0

The two numbers whose square is

4

are

-2

and

2

Domain constraints:

x \in ℝ \ {-2, 2}

▶Solution:

x \in (-2, 1) \cup (2, +∞)