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.<br /><br />First, let's factor the denominator:<br />\[ x^2 - 9x + 14 \]<br /><br />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:<br />\[ x^2 - 9x + 14 = (x - 7)(x - 2) \]<br /><br />So, the function becomes:<br />\[ g(x) = \frac{5 + 7x}{(x - 7)(x - 2)} \]<br /><br />The vertical asymptotes occur at the values of \( x \) that make the denominator zero. Setting each factor equal to zero gives us:<br />\[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \]<br />\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]<br /><br />Thus, the vertical asymptotes are at \( x = 7 \) and \( x = 2 \ sum of the vertical asymptotes is:<br />\[ 7 + 2 = 9 \]<br /><br />Therefore, the sum of the vertical asymptotes of the function is:<br />\[ \boxed{9} \]