Question 1048416
If {{{m(x)= (x+5)/(x-1)}}} and{{{ n(x) = (x -3)}}}, 

{{{m(x)= (x+5)/(x-1)}}}-> since denominator cannot be equal to zero, exclude 

{{{x=1}}}, so domain is { {{{x}}} element  {{{R}}}: {{{x<>1}}} }

{{{ n(x) = (x -3)}}}-> since denominator cannot be equal to zero, exclude 

{{{x=3}}}, so domain is { {{{x}}} element  {{{R}}}: {{{x<>3}}} }


which function has the same domain as


 {{{(m _of_ n)(x)=m(n(x))}}}


{{{m(n(x))=m( (x+5)/(x-1) )}}}


{{{m( (x+5)/(x-1) )=(x+5)/(x-1)-3}}}


{{{m( (x+5)/(x-1) )=(x+5)/(x-1)-3(x-1)/(x-1)}}}


{{{m( (x+5)/(x-1) )=(x+5)/(x-1)-(3x-3)/(x-1)}}}


{{{m( (x+5)/(x-1) )=(x+5-(3x-3))/(x-1)}}}


{{{m( (x+5)/(x-1) )=(x+5-3x+3)/(x-1)}}}


{{{m( (x+5)/(x-1) )=(-2x+8)/(x-1)}}}


{{{m( (x+5)/(x-1) )=-2(x-4)/(x-1)}}}


and the domain is: 

{ {{{x}}} element  {{{R}}}: {{{x<>1}}} }

 so,  {{{m(x)}}} have same as domain as {{{(m _of_ n)(x)}}}