When solving a rational inequality, I know I'm supposed to solve the numerator for zero, and the denominator for any number that will result in an undefined value, but what if after solving it, I don't have a denominator to work with?

Question

anonymous · Answer

give example please

anonymous · Answer

The rational inequality is 5/(x+2)>5/x+2/3x

anonymous · Answer

What you wanto to do in this case, is first add the two faractions on the right hand side, to do that you will need a common denominator

anonymous · Answer

Then once you have added those fractions move that term to the left had side of the >

anonymous · Answer

My final result was 0>2x+34, so x>-17.

anonymous · Answer

it makes no difference in that case because it not less than or equal

anonymous · Answer

if you have something like $$\frac{x}{x+3} \le 1 $$

anonymous · Answer

yep, just remeber that whenever you divide you have to flip the inequality sign

anonymous · Answer

then you need to exclude the denominator

anonymous · Answer

What exactly do you mean by exclude?

anonymous · Answer

When solving other problems I usually get a polynomial fraction for example (w^2-16)/(w-3). From this, I can tell that 3 can't be a solution of the inequality because it would yield an undefined result. I also know that by having the numerator equal to 0, I can the points I will use as a reference in this particular example it would be w^2-16=0, or w^2=16, which w could be +-4. In the original case I did not have a denominator to work, does that mean that I should only use -17 as a reference point?