Answer:
x=-7 and x=5.
Step-by-step explanation:
We have been given a rational function: [tex]f(x)=\frac{x^2+5x+2}{x^2+2x-35}[/tex]. We are asked to find the points at which our function is discontinuous.
A rational function is discontinuous when the function is undefined or the denominator is zero.
Let us find what values of x will make our denominator zero.
[tex]x^2+2x-35=0[/tex]
We will use factoring to find the zeros of x. By splitting the middle term we will get,
[tex]x^2+7x-5x-35=0[/tex]
[tex]x(x+7)-5(x+7)=0[/tex]
[tex](x+7)(x-5)=0[/tex]
[tex](x+7)=0\text{ or }(x-5)=0[/tex]
[tex]x=-7\text{ or }x=5[/tex]
Therefore, at x equals -7 and x equals 5 our function is discontinuous.
