Answer to Question #300982 in Calculus for golden

Question

why will f(x)= x^2+7xz=10/x^3+7x^2+10x have at least one point discontinuity? THE SLASH IS THE FRACTION SYMBOL.. make the answer small, please.

Answer 1

$$f(x)=\dfrac{x^2+7x+10}{x^3+7x^2+10x}$$

$$=\dfrac{(x+2)(x+5)}{x(x+2)(x+5)}$$

$$x\not=0, x\not=-2, x\not=-5$$

The function $f(x)$ has the discontinuities at $x=-5, x=-2,$ and $x=0.$