Dividing by Zero Examples

For what values of x is the following expression undefined?

Newsflash: A fraction is undefined when the denominator equals 0. Dividing by 0 is the biggest math no-no in the book.

The denominator is just x, so this expression is undefined when x = 0.

For what values of x is the following expression undefined?

A fraction is undefined when the denominator equals 0, so we can set the denominator equal to 0 and then solve for x.

7x – 6 = 0

Now add 6 to both sides.

7x – 6 + 6 = 0 + 6
7x = 6

When we divide by 7, we see that makes this expression is undefined.

Which expression is undefined when x = -5?

a.
b.
c.
d.

We can replace the x in each expression with -5. If it makes the denominator equal 0, then the expression is undefined at x = -5. Let's take it one equation at a time.

a. 

Nope, not undefined. The fraction equals 0, but that's not the same thing as dividing by 0.

b. 

Nope, still good.

c.

Ah, there we go. A 0 in the denominator means our fraction implodes in a puff of undefined smoke.

And just for fun…

d.

That one's totally defined, too. The only answer is c.