SOLUTION: i need to solve for this equation: ((x+1)/x-2))+((x-3)/(x-1))<0

Question 588367: i need to solve for this equation:
((x+1)/x-2))+((x-3)/(x-1))<0

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

Maybe we could get a common denominator:

And we could do those multiplications in the numerator:

And we could add the two fractions:

The numerator is always positive.
We can see that has no real roots because the discriminant is negative:

is positive for x=0 (it's 5), and everywhere else.
For to be negative, the denominator has to be negative.
Each factor has a zero (x=1 and x=2), is negative for lesser x values and positive for greater values.
The product will be negative for x such that .
For x=1 and x=2, the denominator is zero and the functions do not exist.
For x<1 and x>2 the function is positive.
So the solution is
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