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

Accepted Solution

Answer:The points of discontinuity are: x=5 and x=1. The point of discontinuity x=5 can be removable.Step-by-step 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.                                         [tex]y= (x-5)/(x^2 - 6x + 5)[/tex]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: [tex]y=1/(x-1)[/tex], so we removed the point of discontinuity x=5.