Question

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

Answer 1

The points of discontinuity are: x=5 and x=1. The point of discontinuity x=5 can be removable.

Explanation:

The points of discontinuity are those points where the function is not defined. To find such points, we should factorize the denominator of the function needs to be factorized.

`y= (x-5)/(x^2 - 6x + 5)`

Considering the quadratic equation of the form ax^2+bx+c =0, then using the quadratic (see attached image), where a=, b=- and c=5, we have that the roots are:

x=5 and x=1.

If we simplify the fraction, by removing the term (x-5) from both the numerator and the denominator, we get:
`y=1/(x-1)`, so we removed the point of discontinuity x=5.