Algebra question

Question

consider (3x+1)/(2x^2+x-6)

find all numbers that are not in the domain 

write the domain Using set builder notation. 

Answer 1

this is a rational expression, defined as long as denominator not = 0

 

factor the denominator: 2x² + x - 6 = (2x - 3)(x +2) = 0 (set to zero to find out how denominator could be 0).

 

this gives us zeros (roots) of -2 and 3/2.  these two values must be excluded from the domain.