Consider the following functions.

$f(x)=\frac{1}{x-2},g(x)=\frac{1}{x}-9$

$($a$)$ Find $(f+g)(x).$

$(f+g)(x)=$

State the domain of the function. $($Enter your answer using interval notation.$)$

$($b$)$ Find $(f-g)(x).$

$(f-g)(x)=$

State the domain of the function. $($Enter your answer using interval notation.$)$

$($c$)$ Find $(fg)(x).$

$(fg)(x)=$

State the domain of the function. $($Enter your answer using interval notation.$)$

$($d$)$ Find $(\frac{f}{g})(x).$

$(\frac{f}{g})(x)=$

State the domain of the function. $($Enter your answer using interval notation.$)$