The domain of a function are all the numbers that can go into the function. In this case we have the given function:
[tex]\frac{6x^2-13x-5}{x+7}[/tex]When you have a function with a variable in the denominator, you have to set the bottom equal to zero and then exclude the x-values you find when you solve the equation:
[tex]\begin{gathered} x+7=0 \\ \text{subtract 7 from both sides} \\ x+7-7=0-7 \\ x=-7 \end{gathered}[/tex]Thus, the domain is all real numbers except -7 (option c)
