Question 119983
{{{f(x)/g(x)}}} Start with the given composition



{{{(16-x^2)/(4-x)}}} Plug in {{{f(x)=16-x^2}}} and {{{g(x)= 4-x}}}


{{{((4+x)(4-x))/(4-x)}}}   Factor {{{16-x^2}}} to get {{{(4+x)(4-x)}}} 



{{{(4+x)(4-x)/(4-x)}}} Combine the fractions



{{{(4+x)cross((4-x))/cross((4-x))}}} Cancel like terms



{{{4+x}}} Simplify



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Answer:


So {{{(16-x^2)/(4-x)}}} simplifies to {{{4+x}}} . In other words {{{(16-x^2)/(4-x)=4+x}}}




So the domain of {{{4+x}}} is x can be any number except x cannot be equal to 4 since that makes the denominator zero for  {{{(16-x^2)/(4-x)}}}