Question

Algebra help please! Identify the restricted domain value(s). picture below

Answer 1

In general when I have a fraction,\[\Large\rm \frac{stuff}{other~stuff \qquad\leftarrow}\]This other stuff is where I have to be really careful.
This other stuff cannot be zero.
We cannot divide by zero in the land of math.

Answer 2

This idea of restrictions can be a little tricky to get used to.
You're LETTING the bottom equal zero, and that tells you what values are not allowed.

Answer 3

So for your problem, we would set our denominator equal to zero,\[\Large\rm x-4=0\]And solve for x.
This will give us our restriction(s).
What do you get?

Answer 4

is it 4? @zepdrix

Answer 5

x=4,
Ok good :)
So we've determined that x=4 cannot be included in our domain.
That is our restriction.

Answer 6

is that the only restriction? and how do i simplify the function? @zepdrix

Answer 7

@zepdrix
@Zero111

Answer 8

Yes, that appears to be the only restriction :)

\[\Large\rm \frac{x^2-2x-8}{x-4}\]
To simplify we need to first factor the numerator.
Then we'll look for matching factors in the top and bottom.