document.write( "Question 59178: Find the domain of the rational function:
\n" ); document.write( "f(x) = (2x^2 - 4) / (3x^2 + 6x - 45) \n" ); document.write( "

Algebra.Com's Answer #40611 by funmath(2933) $\"\"$ $\"About$

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Find the domain of the rational function:
\n" ); document.write( " $\"f%28x%29=%282x%5E2-4%29%2F%283x%5E2%2B6x-45%29\"$
\n" ); document.write( "The domain of a simple rational function is all real numbers EXCEPT the numbers that make the denominator equal 0.
\n" ); document.write( " $\"3x%5E2%2B6x-45=0\"$
\n" ); document.write( " $\"3%28x%5E2%2B2x-15%29=0\"$
\n" ); document.write( " $\"%283%2F3%29%28x%5E2%2B2x-15%29=0%2F3\"$
\n" ); document.write( " $\"x%5E2%2B2x-15=0\"$
\n" ); document.write( "(x+5)(x-3)=0
\n" ); document.write( "x+5=0 and x-3=0
\n" ); document.write( "x=-5 and x=3 will make the denominator 0 and the fraction undefined.
\n" ); document.write( "Therefore the domain includes all real numbers except:-5, and 3.
\n" ); document.write( "set builder notation:{x|x not= -5,3}
\n" ); document.write( "interval notation:(-infinity,-5)U(-5,3)U(3,infinity)
\n" ); document.write( "Happy Calcualting!!! \n" ); document.write( "

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