x-3/x+5<=0

Question

solve and graph the rational inequalitie

Answer 1

Hi Dymond,

Please use parentheses to specify! I am assuming that the expression is (x - 3)/(x + 5) <= 0
First of all, since this is a rational expression, the value of x that makes the denominator 0 can not be in the solution so x = -5 is excluded.

Now, let's find what makes the denominator negative. x+5 <= 0 so x<= -5

Now, let's find what makes the numerator negative. x - 3 <= 0 so x <= 3.

It looks like the answer might be x <= 3 excluding -5. However, the tricky part is to remember that when both the numerator and the denominator are negative, then the quotient will be positive. The range that satisfies negative or zero quotient for the expression is

-5 < x <=3

To help you graph it, there is a vertical asymptote at x = -5 and a horizontal asymptote at y = 1. I believe that you can graph it with all this information.