standard 9 homework\nscore: 6/27 answered: 6/20\nquestion 7\nfind the vertical asymptote(s) of (…

standard 9 homework\nscore: 6/27 answered: 6/20\nquestion 7\nfind the vertical asymptote(s) of ( f(x)=\frac{8 x - 1}{x^{2}+9 x + 14} ).\nthe vertical asymptote(s) are ( x=) \nif there is more than one asymptote, enter your answers separated by a comma.\nquestion help: message instructor post to forum

standard 9 homework\nscore: 6/27 answered: 6/20\nquestion 7\nfind the vertical asymptote(s) of ( f(x)=\frac{8 x - 1}{x^{2}+9 x + 14} ).\nthe vertical asymptote(s) are ( x=) \nif there is more than one asymptote, enter your answers separated by a comma.\nquestion help: message instructor post to forum

Answer

Explanation:

Step1: Factor the denominator

We factor (x^{2}+9x + 14). Using the formula (x^{2}+(a + b)x+ab=(x + a)(x + b)), where (a = 2) and (b=7) (since (2\times7 = 14) and (2 + 7=9)). So, (x^{2}+9x + 14=(x + 2)(x + 7)).

Step2: Find the values that make the denominator zero

Set the denominator equal to zero: ((x + 2)(x + 7)=0). Using the zero - product property (ab = 0) implies (a = 0) or (b = 0). If (x+2=0), then (x=-2). If (x + 7=0), then (x=-7). The numerator (8x-1) is not zero when (x=-2) ((8\times(-2)-1=-16 - 1=-17\neq0)) and when (x=-7) ((8\times(-7)-1=-56 - 1=-57\neq0)).

Answer:

(-2,-7)