# Homework Help: Solving inequalities algebraically, when root is 0

1. Mar 25, 2013

### supernova1203

1. The problem statement, all variables and given/known data
Solve each inequality without graphing the corresponding function.

State the solution algebraically and graph on a number line:

x/x2-9≤0

so i factor out the denominator and get (x+3)(x-3) the root here is zero, but for some reason in the chart (for rational/reciprocal functions) they seem to treat the vertical asymptotes (x=-3, x=3) as root as well... so really instead of having 1 root, of 0, you now have what look like 3 roots, at x=0, x=-3, x=+3

Now i've only learned how to solve inequalities algebraically this morning from this very helpful youtube video:

and according to this 'method' which i like VERY much....i keep getting the wrong answer/sum for the positives/negative intervals if the zero is equal to 0

the book already shows me what the solution is i just dont know how to deal with these roots of 0 in situations like these, can anyone help?

anything would be greatly appreciated, thanks :)

2. Mar 25, 2013

### altamashghazi

for zero solution mark zero on the number line and proceed

3. Mar 25, 2013

### supernova1203

oh hey...i think your right...even if just move in the general direction it will tell me weather or not its positive or negative...

and then i can multiply all the postives/negatives and determine weather the graph in that interval is above 0 or below 0

thanks

4. Mar 25, 2013

### SammyS

Staff Emeritus
You have written your algebraic expression incorrectly.

x/x2-9 is technically equivalent to $\displaystyle \ \frac{x}{x^2}-9\$ which is $\displaystyle \ \frac{1}{x}-9\ .$

You need to use parentheses and write x/(x2-9) which is $\displaystyle \ \frac{x}{x^2-9}\ .$
For a rational expression, the critical points are the roots of the numerator together with the roots of the denominator.

This is because the sign of a rational expression will change if either the numerator or denominator changes sign.