Question 906111
{{{ Let f(x) }}} = {{{ 1/(x+6) }}} and {{{ g(x) = 6x/(x+6) }}}


Find domain of: 
{{{ f(x)+g(h)  = 1/(x+6)+6x/(x+6)= (1+6x)/(x+6) }}}
since denominator cannot be equal to zero, exclude value of {{{x}}} that makes {{{x+6=0}}} => for {{{x=-6}}} denominator will be equal to zero 

so, domain is: { {{{x}}} element {{{R}}} :  {{{x<>-6}}} }


{{{ f(x) - g(x)  = 1/(x+6)-6x/(x+6)= (1-6x)/(x+6)   }}}

domain is same as above: { {{{x}}} element {{{R}}} :  {{{x<>-6}}} }


{{{ f(x) * g(x) = 1/(x+6)*6x/(x+6) =  6x/(x+6)^2 }}} 

{{{(x+6)^2=0}}} for {{{x=-6}}}

so,domain is same as above: { {{{x}}} element {{{R}}} :  {{{x<>-6}}} }


{{{ f(x)/g(x)  = (1/(x+6))/(6x/(x +6)) = 1( x+6)/(6x( x+6))=1cross((x+6))/(6x*cross(( x+6)))= 1/6x }}}

here we also have denominator {{{x+6}}}, so exclude {{{x=-6}}} like above

than we got denominator {{{6x}}} that will be equal to zero if {{{x=0}}},exclude this one too

so, domain is: { {{{x}}} element {{{R}}} : {{{x<>-6}}} and {{{x<>0}}} }