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what are the points of discontinuity? are they all removable? y= (x-5) / x^2 - 6x + 5

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2033
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what are the points of discontinuity? are they all removable?  y= (x-5) / x^2 - 6x + 5

Apr 26, 2015

#1
+129690
+10

Note......

(x - 5) / [ x^2 - 6x + 5] =

(x - 5) / [ (x - 1) (x -5) ] =

1 / (x - 1)

There will be a "hole" at x = 5......but the discontinuity at x = 1  isn't "removable".....there's a vertical asymptote at that point......

Here's the graph.......

https://www.desmos.com/calculator/m598ibdrql

{Believe me....there is a "hole" at x = 5  !!!}

Apr 26, 2015

#1
+129690
+10

Note......

(x - 5) / [ x^2 - 6x + 5] =

(x - 5) / [ (x - 1) (x -5) ] =

1 / (x - 1)

There will be a "hole" at x = 5......but the discontinuity at x = 1  isn't "removable".....there's a vertical asymptote at that point......

Here's the graph.......

https://www.desmos.com/calculator/m598ibdrql

{Believe me....there is a "hole" at x = 5  !!!}

CPhill Apr 26, 2015
#2
+118622
0

I have never heard of the term "removable" in relation to discontinuities

Apr 26, 2015