Answer:The domain = {x : x ≠ -5 , 7}Step-by-step explanation:- The domain of the function is the values of x which makes the function defined- If the function has a denominator then the domain is all the values of x except the zeroes of the denominator- Zeroes of the denominator means the values of x when the denominator = 0- The function is [tex]y=\frac{6+9x}{(6-Ix-1I)}[/tex]- To find the domain of the function find the zeroes of the denominator∵ The denominator is ⇒ 6 - Ix - 1I∴ 6 - Ix - 1I = 0- Subtract 6 from both sides∴ - Ix - 1I = -6- Multiply both sides by -1∴ Ix - 1I = 6- The absolute value of x - 1 = 6 that means x - 1 = 6 OR x - 1 = -6∵ x - 1 = 6- Add 1 to both sides∴ x = 7∵ x - 1 = -6- Add 1 to both sides∴ x = -5∴ The zeroes of the denominator are -5 and 7∵ x = -5 and x = 7 make the denominator = 0- Any value divided by 0 is undefined∴ x can be any value except -5 and 7∴ The domain of the function is all real values of x except -5 and 7* The domain = {x : x ≠ -5 , 7}