Question

Where is the hole in the equation (x-2)/(x^2-4)

Answer 1

x = 2, or at the point (2, 1/4)

Explanation:

Factor the denominator (difference of two squares).

`(x-2)/(x^2-4) = (x-2)/((x-2)(x+2))`

There is a common factor of
`x-2` which indicates there is a hole at
`x=2` (where
`x-2=0`).

If you're used to answering a question like this with the complete coordinates of a point, put
`x=2` into a simplified fraction, by cancelling the common factor.

Substitute 2 for x.

`(1)/(x+2) = (1)/(2+2) = (1)/(4)`

The hole is at the point (2, 1/4).