## Calculus, 10th Edition (Anton)

$$f(x)=\frac{5}{x}+\frac{2 x}{x+4}$$ is continuous for all real numbers $x$ except $x = 0$, $x = -4$.
$$f(x)=\frac{5}{x}+\frac{2 x}{x+4}$$ suppose $$f(x)=g(x)+h(x)$$ such that $$g(x)= \frac{5}{x} , \quad \quad h(x)=\frac{2 x}{x+4}$$ Solving the equation $$x+4=0$$ yields discontinuities at $x = -4$. Therefore the function $$h(x)=\frac{2 x}{x+4}$$ is continuous for all real number $x$ except $x = -4$ Thus $$f(x)=\frac{5}{x}+\frac{2 x}{x+4}$$ is continuous for all real numbers $x$ except $x = 0$, $x = -4$. Finally, values of $x$, at which $f$ is not continuous are $x = 0$, $x = -4$.