# How do you find the removable discontinuity(hole) for the graph of #y=(x^2 - 9x -10)/ (2x^2 - 2)#?

Factoring the numerator and denominator reveals a common factor of

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To find the removable discontinuity (hole) for the graph of y=(x^2 - 9x -10)/ (2x^2 - 2), we need to factor both the numerator and denominator. Factoring the numerator, we get (x - 10)(x + 1). Factoring the denominator, we get 2(x - 1)(x + 1).

We can see that (x + 1) appears in both the numerator and denominator. Therefore, there is a removable discontinuity (hole) at x = -1. To find the y-coordinate of the hole, we substitute x = -1 into the simplified expression (x - 10)/(2(x - 1)). Simplifying this expression, we get y = -11/2.

Therefore, the removable discontinuity (hole) for the graph of y=(x^2 - 9x -10)/ (2x^2 - 2) is at the point (-1, -11/2).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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