English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

solve the inequality (2x + 1/ x^2 - 4) > 0

any help is appreciated!!!!
some sort of explaination

2007-03-02 01:13:23 · 2 answers · asked by ztaylor8283 1 in Science & Mathematics Mathematics

2 answers

Assuming you mean (2x +1)/(x^2 - 4) > 0:
A fraction is greater than 0 iff both its numerator and its denominator are of the same sign.

2x + 1 is greater than 0 for:
2x + 1 > 0
2x > -1
x > -1 / 2

x^2 - 4 is greater than 0 for:
x^2 - 4 > 0
x^2 > 4
x < -2 or x > 2

Therefore, both numerator and denominator are greater than 0 when
x > -1 / 2 AND (x < -2 or x > 2), so when
-> x > 2

Since 2x + 1 is greater than 0 when x > -1 / 2, it is less than 0 when
x < -1 / 2

Since x^2 - 4 is greater than 0 when x < -2 or x > 2, it is less than 0 when
-2 < x < 2

Therefore, both are less than 0 (and hence the fraction is greater: a negative divided by a negative is a positive) when
x < -1 / 2 AND -2 < x < 2, so
-> -2 < x < -1 / 2

Combining these, the inequality is true when
-2 < x < -1 / 2 or x > 2

2007-03-02 01:15:55 · answer #1 · answered by Phred 3 · 0 1

First x^2-4 not 0 so x not +-2.The function changes it sign at
-2 , -1/2 ,and2.

the sign is -infinity - ( -2) + ( -1/2) - (2) +
So your solution is
-22
You should remember that a quotient a a product have the same sign.So with the remark (first) you can study the sign of

(2x+1)*(x^2-4)

2007-03-02 13:41:23 · answer #2 · answered by santmann2002 7 · 0 0

fedest.com, questions and answers