Search 74,102 tutors
FIND TUTORS
Ask a question
0 0

7/x-3 + 2x/x+3 < -1

Tutors, please sign in to answer this question.

1 Answer

7/(x-3) + 2x/(x+3) < -1
 
7(x+3)/((x+3)(x-3)) + 2x(x-3)/((x+3)(x-3))  + 1 < 0
 
(7(x+3) + 2x(x-3))/(x^2-9) + (x^2-9)/(x^2-9) < 0
 
(7x + 21 + 2x^2 - 6x + x^2 - 9)/(x^2-9) < 0
 
(3x^2 + x + 12)/(x^2-9) < 0
 
h = -1/(2*3) = - 1/6
k = 12 - 3(-1/6)^2 = 12 - 1/12 > 0
 
3 > 0 and k > 0 ==> numerator always positive.
 
So denominator determines sign of fraction:
 
x^2 - 9 < 0
 
x^2 < 9
 
|x| < 3
 
-3 < x < 3 is solution.
 
In interval notation: x ∈ (–3,3).