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

1 Answer
Dec 2, 2015

Answer:

Solve #F(x) = (x + 5)^2/(x^2 - 4) >= 0#

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

Explanation:

#F(x) = (x + 5)^2/((x - 2)(x + 2)) >= 0#.
This function is undefined when #x = +- 2#
Solve this inequality algebraically by using a sign chart.
Call #f(x) = (x + 5)^2# . This function is always positive
Call #g(x) = (x - 2)(x + 2)#. This g(x) = 0 when #x = +-2#
g(x) < 0 between (-2) and (2).
Sign Chart. of #F(x) = f(x)/(g(x))#
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).

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