# How do you determine the value of #A# such that #f(x)# has a point discontinuity without using trial and error?

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#f(x)=(x^2+2x+A)/(x^2-4x-5)#

##### 1 Answer

#### Explanation:

A point of discontinuity is also known as a hole. For example, the graph of

The trick about holes is that they occur when a common factor is cancelled out in the numerator and the denominator.

Start by factoring the expression that we know: the denominator.

Now let's compare this to the numerator. There is no way that we can make

To make

Let's do a final check.

So, there will be a discontinuity at

Hopefully you understand now!