How do solve 3/(x-2)<=3/(x+3) algebraically?
1 Answer
Oct 5, 2016
Explanation:
Slower way:
-
Bring everything to the right:
3/(x-2) - 3/(x+3) \leq 0 -
Lowest common denominator:
(3(x+3)-3(x-2))/((x-2)(x+3))\leq 0 -
Expand the numerator:
(3x+9-3x+6)/((x-2)(x+3))\leq 0 -
(9+6)/((x-2)(x+3))\leq 0 -
(15)/((x-2)(x+3))\leq 0 -
Since
15 is always positive, the sign of the fraction is decided by the sign of the denominator.(x-2)(x+3) represents a parabola with zeros inx=-3 andx=2 . Such a parabola is negative between its solutions, as you can see in the graph here:
graph{(x-3)(x+2) [-4.96, 6.146, -2.933, 2.614]}