Find domain of?

Question

find the domain of 1-x^2-5x/x

Answer 1

the domain is basically "all real numbers except what will cause division by zero"

if you set the denominator equal to zero, you'll get what is disallowed.

In this case, x = 0 is disallowed

Domain, then is {x|x is a real number, not 0}

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One warning: if you have an equation like y=(x-1)(x+1)/(x-1), you can divide out the x-1 on top and bottom (since (x-1)/(x-1)=1 and get y=(x+1) BUT THE DOMAIN IS BASED ON THE ORIGINAL EQUATION; it's still {x|x is a real number, not 1}

Answer 2

When you simplify the last term, you get 1 - x^2 - 5, so
your expression will be -x^2 - 4.

The domain consists of all the numbers you're allowed to use for x. There's nothing here to prevent any number from being used, so your domain is all the real numbers.

If the x in the denominator in the last term didn't divide out, your domain would be all real numbers except 0 because a denominator can't be 0.

Answer 3

x not equal to zero.