Thread: Solving Rational Inequalities

Solve the inequality: 2x-10/x >x+5
I tried it and got an unfactorable polynomial: x^2+3x+10, but the answer says it's x<-5 and -2<x<0.
Thanks in advance!

What is the question and what have you tried?

or is it

Originally Posted by Dragon08

Solve the inequality: 2x-10/x >x+5
I tried it and got an unfactorable polynomial: x^2+3x+10, but the answer says it's x<-5 and -2<x<0.
Thanks in advance!

To get the book answer, the problem would have to be equivalent to solving:

It's the first one, and I made the moved x+5 onto the left side and made a common denominator. The resulting polynomial numerator is unfactorable.

To SammyS: Oh, then the the book's answer may be wrong.

First of all, like SammyS said it has to be -2x in the numerator of the RS, because if it's 2x then you'll get a negative discriminant and so no roots in .

Rational inequality
and

Solve:


Now you can make a sign table to determine the solution.

Originally Posted by Siron

First of all, like SammyS said it has to be -2x in the numerator of the RS, because if it's 2x then you'll get a negative discriminant and so no roots in .

Rational inequality
and

Solve:


Now you can make a sign table to determine the solution.

Good spot on the -2x instead of 2x (Clap)

Alternatively, if then we need to change the direction of the inequality when multiplying through by x.