standard 9 homework\nscore: 7/27 answered: 7/20\nquestion 8\nfind the vertical asymptotes and holes…

standard 9 homework\nscore: 7/27 answered: 7/20\nquestion 8\nfind the vertical asymptotes and holes (removable discontinuities) of the rational function.\n$f(x)=\\frac{x - 10}{(x - 7)(x + 8)}$\nthe holes are at $x=$\nthe vertical asymptotes are $x=$\nif there is more than one of each, enter your answers separated by a comma. if there is not a hole or\nasymptote, enter dne.\nquestion help: message instructor post to forum

standard 9 homework\nscore: 7/27 answered: 7/20\nquestion 8\nfind the vertical asymptotes and holes (removable discontinuities) of the rational function.\n$f(x)=\\frac{x - 10}{(x - 7)(x + 8)}$\nthe holes are at $x=$\nthe vertical asymptotes are $x=$\nif there is more than one of each, enter your answers separated by a comma. if there is not a hole or\nasymptote, enter dne.\nquestion help: message instructor post to forum

Answer

Explanation:

Step1: Analyze holes

Holes occur when a factor cancels in numerator and denominator. Here, numerator (x - 10) and denominator ((x - 7)(x + 8)) have no common factors. So, holes: (x=\text{DNE})

Step2: Analyze vertical asymptotes

Vertical asymptotes occur where denominator is zero (after canceling common factors). Set ((x - 7)(x + 8)=0). Using zero - product property (x-7 = 0) gives (x = 7) and (x+8=0) gives (x=-8)

Answer:

The holes are at (x=\text{DNE}). The vertical asymptotes are (x = 7,-8)