document.write( "Question 559661: hi what would the domain of 5x/x^3+36x be i've tried to find what number would give me 36 but i don't know if that's the right method \n" ); document.write( "

Algebra.Com's Answer #363492 by KMST(5347) $\"\"$ $\"About$

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The domain of f(x) = 5x/(x^3+36x) = $\"5x%2F%28x%5E3%2B36x%29\"$
\n" ); document.write( "includes all real numbers except those that make $\"x%5E3%2B36x=0\"$
\n" ); document.write( "Factoring, we get:
\n" ); document.write( " $\"x%5E3%2B36x=0\"$ ==> $\"x%28x%5E2%2B36%29=0\"$
\n" ); document.write( "In the real numbers there are no solutions for
\n" ); document.write( " $\"x%5E2%2B36=0\"$ , so the only solution would be $\"x=0\"$ .
\n" ); document.write( "For $\"x=0\"$ , the function does not exist; it's undefined.
\n" ); document.write( "For any other value of $\"x\"$ , we can simplify to
\n" ); document.write( "f(x) = $\"5x%2F%28x%28x%5E2%2B36%29%29\"$ = $\"5cross%28x%29%2F%28cross%28x%29%28x%5E2%2B36%29%29\"$ = $\"5%2F%28x%5E2%2B36%29\"$
\n" ); document.write( "The graph of the function is the same as the graph of
\n" ); document.write( "f(x) = $\"5%2F%28x%5E2%2B36%29\"$ , except that it does not exist for $\"x=0\"$ .
\n" ); document.write( "There is a hole where (0,5/36) would be.
\n" ); document.write( "The number $\"x=0\"$ is the only real number excluded from the domain of the function. \n" ); document.write( "

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