# How do you solve (x+5)^2 /( x^2-4 )>=0?

Dec 2, 2015

Solve $F \left(x\right) = {\left(x + 5\right)}^{2} / \left({x}^{2} - 4\right) \ge 0$

Ans: Open intervals: (-inf, -2) and (2, +inf)

#### Explanation:

$F \left(x\right) = {\left(x + 5\right)}^{2} / \left(\left(x - 2\right) \left(x + 2\right)\right) \ge 0$.
This function is undefined when $x = \pm 2$
Solve this inequality algebraically by using a sign chart.
Call $f \left(x\right) = {\left(x + 5\right)}^{2}$ . This function is always positive
Call $g \left(x\right) = \left(x - 2\right) \left(x + 2\right)$. This g(x) = 0 when $x = \pm 2$
g(x) < 0 between (-2) and (2).
Sign Chart. of $F \left(x\right) = f \frac{x}{g \left(x\right)}$
Sign of F(x) is the resultant sign of f(x) and g(x).
F(x) is positive in interval (-inf, -2) and F(x) > 0 inside (2, +inf).
Ans: Open Intervals: (-inf, -2) and (2, +inf).