SOLUTION: {{{ (12x^2-4)/((x^2-1)^3) <= 0 }}}For which of the following values of x does the inequality above hold? a. 0 b. 3/5 c. 3/4 d. &#8722;1/2 e. &#8722;3/4 f. -10

Algebra ->  Equations -> SOLUTION: {{{ (12x^2-4)/((x^2-1)^3) <= 0 }}}For which of the following values of x does the inequality above hold? a. 0 b. 3/5 c. 3/4 d. &#8722;1/2 e. &#8722;3/4 f. -10       Log On


   

Question 989675: +%2812x%5E2-4%29%2F%28%28x%5E2-1%29%5E3%29+%3C=+0+For which of the following values of x does the inequality above hold?
a. 0
b. 3/5

c. 3/4
d. −1/2
e. −3/4

f. -10
g. 1
h. −9/10

Please explain why
Thank you
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Pay most attention to the numerator. THAT needs to be less than or equal zero.

12x%5E2-4%3C=0
12x%5E2%3C=4
3x%5E2%3C=1
x%5E2%3C=1%2F3
x=0%2B-+sqrt%281%2F3%29-----the critical value.


3x%5E2-1 is a parabola, less than 0 AT and BETWEEN the roots.
Roots found were -sqrt%281%2F3%29 and sqrt%281%2F3%29;
Rationalized, -sqrt%283%29%2F3 and sqrt%283%29%2F3.

ANSWER:
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Note that the denominator must not be zero, so x%3C%3E1.
Otherwise, -sqrt%283%29%2F3%3C=x%3C=sqrt%283%29%2F3 BUT x%3C%3E1 and x%3C%3E-1.
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