SOLUTION: given: f(x)= x2+x-6/x2+8x+15 Write the solution set in the blank using interval notation for f(x)>0 The (x2) parts in the problem mean (x squared) The f(x)>0 is

Algebra ->  Rational-functions -> SOLUTION: given: f(x)= x2+x-6/x2+8x+15 Write the solution set in the blank using interval notation for f(x)>0 The (x2) parts in the problem mean (x squared) The f(x)>0 is      Log On


   

Question 318664: given:

f(x)= x2+x-6/x2+8x+15
Write the solution set in the blank using interval notation for f(x)>0
The (x2) parts in the problem mean (x squared)
The f(x)>0 is supposed to be (greater than or equal to) not just greater than
Thank you for taking the time to look at this, appreciate it alot.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+%28x%5E2%2Bx-6%29%2F%28x%5E2%2B8x%2B15%29
f%28x%29=+%28%28x%2B3%29%28x-2%29%29%2F%28%28x%2B3%29%28x%2B5%29%29
f%28x%29=+%28x-2%29%2F%28x%2B5%29
Break up the number line into three parts.
Region 1: (-infinity,-5)
Region 2: (-5,2)
Region 3: (2,infinity)
Pick a point in each region (not at the endpoints) and test the function.
If it solves the equation, it's in the solution region.
Region 1: x=-10
%28x-2%29%2F%28x%2B5%29%3E0
%28-10-2%29%2F%28-10%2B5%29%3E0
%28-12%29%2F%28-5%29%3E0
12%2F5%3E0
True, Region 1 is part of the solution.
.
.
.
Region 2: x=0
%28x-2%29%2F%28x%2B5%29%3E0
%28-2%29%2F%285%29%3E0
%28-2%29%2F%285%29%3E0
False, Region 2 is not part of the solution.
.
.
.
Region 3: x=5
%28x-2%29%2F%28x%2B5%29%3E0
%285-2%29%2F%285%2B5%29%3E0
%283%29%2F%2810%29%3E0
True, Region 3 is part of the solution.
.
.
.
(-infinity,-5) U (2,infinity)
.
.
Graphical verification of the results.
.
.
.