Answer:
x ≠ -3
and
x ≠ 1
Step-by-step explanation:
the rational expression is:
[tex]\frac{x^2+x+6}{x^2+2x-3}[/tex]
a domain restriction will be when the denominator is equal to zero:
[tex]x^2+2x-3=0[/tex]
so we must find the two values of x that makes the expreesion for the denominator equal to zero.
we can do this by factoring:
[tex]x^2+2x-3=(x+3)(x-1)=0[/tex]
and now we use the zero factor property, which means that if
[tex](x+3)(x-1)=0[/tex]
we have two solutions:
[tex]x+3=0\\x=-3[/tex]
and
[tex]x-1=0\\x=1[/tex]
thus, when [tex]x=-3[/tex] or [tex]x=1[/tex] the denominator is zero. so in the domain we cannot have [tex]x=-3[/tex] or [tex]x=1[/tex] .
So the domain restrictions are:
x ≠ -3
and
x ≠ 1
