For what values of X are undefined

Question

1. x over x + 1
2. x - 3 over x² - 9

Answer 1

#1 You don't want "x" to =-1 because you can't divide by 0.

#2. x - 3 over x² - 9

Here x is not to be 3 or -3.

Answer 2

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