What is the sum of the vertical asymptotes of the function below? g(x)=((5+7x))/(x^2)-9x+14 square

To find the vertical asymptotes of the function \( g(x) = \frac{5 + 7x}{x^2 - 9x + 14} \), we need to determine where the denominator is equal to zero, as these are the points where the function is undefined.First, let's factor the denominator: We look for two numbers that multiply to 14 and add -9. These numbers are -7 and -2. Therefore, we can factor the quadratic expression as follows: So, the function becomes: The vertical asymptotes occur at the values of that make the denominator zero. Setting each factor equal to zero gives us: Thus, the vertical asymptotes are at and \( x = 2 \ sum of the vertical asymptotes is: Therefore, the sum of the vertical asymptotes of the function is: