Question

Y=x-8/x^2+4x-5 find any points of discontinuity for the rational function

Answer 1

Answer:

x=-5, x=1

Step-by-step explanation:

y=x-8/x^2+4x-5

$y=\frac{x-8}{x^2+4x-5}$

When denominator becomes 0 in a rational function then there will be a break in the graph

To find any points of discontinuity for the rational function , we set the denominator =0 and solve for x

x^2 + 4x -5 =0

Now we factor x^2 +4x -5

product is -5  and sum = 4

5 * (-1) = -5

5 +(-1) = 4

(x+5)(x-1) =0

set each factor =0 and  solve for x

x+5=0 , so x= -5

x-1=0 , so x= 1

x=-5, x=1 are the points of discontinuity for the rational function