document.write( "Question 1126016: Solve the inequality using a sign chart. Support graphically. SHow the equations that find the real zeros.
\n" ); document.write( "((x-5)/(x^2-36))<0 \n" ); document.write( "

Algebra.Com's Answer #742361 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( " $\"f%28x%29+=+%28x-5%29%2F%28x%5E2-36%29+=+%28x-5%29%2F%28%28x-6%29%28x%2B6%29%29\"$

\n" ); document.write( "f(x) is 0 at x = 5 only.

\n" ); document.write( "f(x) is undefined (so there are vertical asymptotes) at x=-6 and x=6.

\n" ); document.write( "The zeros of the numerator and denominator divide the domain into four parts: (-infinity,-6), (-6,5], [5,6), and (6, infinity).

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document.write( "                  |  x+6  x-5  x-6  |  f(x)\r\n" );
document.write( "  --------------------------------------------\r\n" );
document.write( "  (-infinity, -6) |   -    -    -   |   -\r\n" );
document.write( "           (-6,5] |   +    -    -   |   +\r\n" );
document.write( "            [5,6) |   +    +    -   |   -\r\n" );
document.write( "    (6, infinity) |   +    +    +   |   +

\n" ); document.write( "The function is negative on (-infinity,-6) and on (5,6); it is 0 at x=5; the value goes to positive or negative infinity close to the vertical asymptotes, at x=-6 and x=6.

\n" ); document.write( "The graph...

\n" ); document.write( " $\"graph%28400%2C400%2C-10%2C10%2C-1%2C1%2C%28x-5%29%2F%28x%5E2-36%29%29\"$ \n" ); document.write( "

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