### Instruction: What is the domain of the function $$\ell(y) = \frac{1}{(y-2)+(y-8)}~?$$ Express your answer in interval notation.### Response: So the denominator of the fraction is $(y-2)+(y-8)$.
And that is equal to $2y-10$.
Yes, so we need to solve the inequality $2y-10\neq0$.
And that inequality is equivalent to $y\neq5$.
Right. So the domain of $\ell$ is the set of real numbers, except for 5.