Simplify and state the domain for the expression. \( \frac{x-5}{x^{2}-15 x+50}=\square \) The domain is all real numbers except If needed, use a commas to separate answers. Question Help: \( \square \) Message instructor

To simplify \( \frac{x-5}{x^{2}-15x+50} \), first factor the denominator. The quadratic can be factored as \( (x-5)(x-10) \). Therefore, the expression simplifies to \( \frac{1}{x-10} \) for \( x \neq 5 \). The domain of the expression is all real numbers except where the denominator is zero. Setting \( x^2 - 15x + 50 = 0 \) gives us \( x = 5 \) and \( x = 10 \). So, the domain is all real numbers except 5, 10.