Answer:
[tex]\displaystyle \frac{x^2+3x+2}{1-x}<0[/tex]
Step-by-step explanation:
Rational Inequality
We are given the solution of rational inequality:
(-2,-1) U (1,∞)
The first set suggests a limited zone than can be obtained by a quadratic equation of the form:
[tex](x-a)(x-b)<0[/tex]
Where a and b are the roots of the equation, which coincide with the endpoints of the interval. Thus, to get the interval, we can use:
[tex](x+2)(x+1)<0[/tex]
Operating:
[tex]x^2+3x+2<0[/tex]
The second set is an open infinite interval, that can be modeled as a third binomial that changes signs in x=1 and is in the denominator, so x=1 is not included.
Thus, one possible inequality is:
[tex]\mathbf{\displaystyle \frac{x^2+3x+2}{1-x}<0}[/tex]
