document.write( "Question 201553: Give the equation of the vertical asymptote(s) of the rational function.\r
\n" ); document.write( "\n" ); document.write( "F(x) = (x-1)/(x^2+4)
\n" ); document.write( " A) x = 1, x = -1
\n" ); document.write( " B) x = 4
\n" ); document.write( " C) x = -4
\n" ); document.write( " D) None
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #151773 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Vertical asymptotes of a rational function, if any, will be for values of x that make the denominator zero.

\n" ); document.write( "For your function we will try to find what values of x make \"x%5E2%2B4\" negative. But if one understands how squaring works we can see that this particular denominator can never be zero because:
  1. When you square zero you get zero. When you square any other Real number you get some positive number. So \"x%5E2\" is either zero or a positive number no matter what x is.
  2. If you add \"x%5E2\", which is zero or positive, to 4 you will always get a positive number, never a zero!
Since the denominator can never be zero, there are no vertical asymptotes for this function.

\n" ); document.write( "If you denominator had been \"x%5E2-4\" instead, we could not say that the denominator could never be zero because subtracting 4 from a zero or positive number could result in a zero. So we would have to solve the equation:
\n" ); document.write( "\"x%5E2-4=0\"
\n" ); document.write( "We could factor this into:
\n" ); document.write( "\"%28x%2B2%29%2A%28x-2%29=0\"
\n" ); document.write( "In order for a product to be zero one of the factors must ne zero so:
\n" ); document.write( "\"x%2B2=0\" or \"x-2=0\"
\n" ); document.write( "Solving each of these we get
\n" ); document.write( "\"x+=+-2\" or \"x=2\"
\n" ); document.write( "These would be the vertical asymptotes for a (simplified) rational function with \"x%5E2-4\" as the denominator (like \"q%28x%29=5%2F%28x%5E2-4%29\"). \n" ); document.write( "
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