Question

Write a rational inequality with the solution: (-2,-1)U(1, oo)

Answer 1

Answer:

$\displaystyle \frac{x^2+3x+2}{1-x}$

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:

$(x-a)(x-b)$

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:

$(x+2)(x+1)$

Operating:

$x^2+3x+2$

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:

$\mathbf{\displaystyle \frac{x^2+3x+2}{1-x}$