Question 660394
{{{f(x) = 5/(x + 4)}}}
 
{{{g(x) = x /(x + 4)}}}
 
 find the domain of {{{(f/g)(x)}}}


{{{(f/g)(x) = (5/(x + 4))/( x /(x + 4))}}}


{{{(f/g)(x) = (5/cross((x + 4)))/( x /cross((x + 4)))}}}


{{{(f/g)(x) = 5/x }}}....as you see, {{{x}}} is denominator, therefore cannot 

be equal to zero

as you can see in {{{f(x) and {{{g(x))), denominator is {{{x+4}}}; therefore 

{{{x }}} cannot be {{{-4}}} 


so, the domain is: {{{x}}} element of {{{R}}}, {{{x<>0}}} and {{{x<>-4}}}



{{{ graph( 600, 600, -10, 10, -10, 10, (5/(x + 4))/( x /(x + 4))) }}}