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

1) Let's solve in

ℝ

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

Let's solve in

ℝ

x - 1 < 0

Solution obtained:

x < 1

2) Let's solve in

ℝ

x^{2} - 4 < 0

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 0^{2} - 4 \cdot 1 \cdot (-4)

Δ = - 4 \cdot (-4)

Δ = 16

Since

Δ > 0

, the equation has two solutions:

For the 1st solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = - \frac{\sqrt{16}}{2}

x1 = - \frac{4}{2}

x1 = -2

Solution second:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{\sqrt{16}}{2}

x2 = \frac{4}{2}

x2 = 2

Solution obtained:

x \in (-2, 2)

Let's create the table of the different solutions to find the overall solution:

▶Solution obtained:

x \in (-∞, -2) \cup (1, 2)