The most common ways for an expression to be undefined at a value of x is for there to be a factor divided by zero.
So we want to find values of x at which the denominator is zero.
For question 1,
x/(x + 1), we need x + 1 = 0
By simply rearranging we have that x = -1
For question 2,
(x - 3)/(x2 - 9), we need x2 - 9 = 0
By applying the difference of squares formula a2 - b2 = (a + b)(a - b)
we get that (x + 3)(x - 3) = 0.
For a product to be equal to zero, one of the factors must be equal to zero.
Then x + 3 = 0 or x - 3 = 0
x = -3 or x = 3.
The expression would be undefined for either of the two values.
Now, for this question, you might be asking
"Hey, there's an x - 3 in the numerator, wouldn't it cancel out with the x - 3 factor in the denominator so only -3 is the right answer?"
But 0/0 is still undefined, so the expression would be equal to 1/(x + 3) for all values of x EXCEPT for x = 3, where it is undefined.
NOTE: 1/(x + 3) itself is undefined at x = -3, so it is both x = 3 and x = -3