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avanturin [10]
3 years ago
6

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

Mathematics
1 answer:
Sonja [21]3 years ago
6 0

Answer:

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

Step-by-step explanation:

Factor the denominator (difference of two squares).

\frac{x-2}{x^2-4} = \frac{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 <u>simplified</u> fraction, by cancelling the common factor.

Substitute 2 for <em>x.</em>

<em />\frac{1}{x+2} = \frac{1}{2+2} = \frac{1}{4}<em />

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

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