# Algebra

posted by Dee Williams

Solve Rational Inequalities

x^2-x-2/x^2+5x+6<0

numerator (x-2)(x+1)
denominator (x+3)(x+2)

numerator/denominator <0 which means the numerator and denominator are of opposite signs.

Case one: X>0
1a 0<x<2 denominator is +, numerator -, so this is valid.
1b 2<x<inf numerator and denomintor are +, inequality is not valid.
numerator (x-2)(x+1)
denominator (x+3)(x+2)
Case two X<0
2a -1 <x<0
numerator is negative, denom is +, so this range is valid for the identity.
2b -2<x<-1
numerator is +, dem is positve, this is an invalid domain.
2c -3<x<-2 numer is +, den is -, so this is a valid region
you do case 2d, -inf <x < -3

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