How do you find the domain of #y = x/(x^2 - 2x -3)#?

1 Answer
Shell
Oct 15, 2016

#(-oo,-1)U(-1,3)U(3,oo)#

Explanation:

Find the domain of

#y=frac{x}{x^2-2x-3}#

To find the domain, find values of x that make the denominator equal to zero. The function is undefined at these values of x, which means these values are not included in the domain.

Set the denominator equal to zero.

#x^2-2x-3=0#

Factor.

#(x-3)(x+1)=0#

Set each factor equal to zero and solve.

#x-3=0# and #x+1=0#

#x=3# and #x=-1#

The domain can be written as #x!=3# and #x!=-1#

or in interval notation

#(-oo,-1)U(-1,3)U(3,oo)#

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