Question 65784
These are rational expressions, the domain of rational expressions contain anything EXCEPT what will make the denominator (bottom) equal 0.

1. 6/4x^3
{{{6/4x^3}}}
The restricted values are found by setting the denominator equal to 0 and solving for x:
{{{4x^3=0}}}
{{{4x^3/4=0/4}}}
{{{x^3=0}}}
cubed root (x^3)= cubed root (0)
x=0
The domain is all real numbers except 0.
{x|x not= 0} <---set builder notation
(-infinity,0)U(0,infinity) <--interval notation
:
2. (x+5)/(x^2-36)
{{{x^2-36=0}}}
{{{x^2-36+36=0+36}}}
{{{x^2=36}}}
{{{sqrt(x^2)=+-sqrt(36)}}}
x=-6 or x=6
{x|x not= +\- 6}
(-infinity,-6)U(-6,6)U(6,infinity)
:
3. (x+5)/(x^2+36)
{{{x^2+36=0}}}
{{{x^2+36-36=0-36}}}
{{{x^2=-36}}}
{{{sqrt(x^2)=+-sqrt(-36)}}}
This results in no real number solution, therefore the domain for this is ALL REAL NUMBERS.
{x|x=R}
(-infinity,infinity)
Happy Calculating!!!