document.write( "Question 1186675: Simplify the following and state any restrictions on the variable.
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Algebra.Com's Answer #817632 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "He's right about the parentheses when typing numerators and denominators all\r\n" );
document.write( "on one line. Otherwise, you can't tell where a numerator or denominator starts\r\n" );
document.write( "and ends.  Here is how you should have typed your problem:\r\n" );
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document.write( "((9x^2 - 64)/(x^2+7x+12)) ÷ ((3x^2+17x+24)/(x^2+6x+9))\r\n" );
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document.write( "Correct punctuation is even more important in math than in English. Anyways,\r\n" );
document.write( "I'll assume what I think you meant to be a numerator and a denominator, and\r\n" );
document.write( "where I think you meant for them to be.\r\n" );
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document.write( "Even after we simplify the expression, we must make restrictions to make sure\r\n" );
document.write( "that there are no numbers we could substitute for x that would cause the\r\n" );
document.write( "original expression to be undefined by dividing by 0. \r\n" );
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document.write( "Therefore, \r\n" );
document.write( "EACH TIME WE CANCEL ANY FACTOR, WE MUST MAKE A RESTRICTION THAT PREVENTS THE\r\n" );
document.write( "CANCELED EXPRESSION FROM EVER BEING EQUAL TO ZERO.  ALSO IN THE FINAL\r\n" );
document.write( "SIMPLIFICATION, WE MUST MAKE A RESTRICTION THAT PREVENTS ITS DENOMINATOR\r\n" );
document.write( "FROM BEING EQUAL TO ZERO.\r\n" );
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document.write( "\"%289x%5E2+-+64%29%2F%28x%5E2%2B7x%2B12%29\" ÷ \"%283x%5E2%2B17x%2B24%29%2F%28x%5E2%2B6x%2B9%29\" \r\n" );
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document.write( "Invert and multiply:\r\n" );
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document.write( "\"%28%289+x%5E2+-+64%29%2F%28x%5E2+%2B+7+x+%2B+12%29%29\"\"%22%22%2A%22%22\"\"%28%28x%5E2+%2B+6+x+%2B+9%29%2F%283+x%5E2+%2B+17+x+%2B+24%29%29\"\r\n" );
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document.write( "Factor:\r\n" );
document.write( "\"%28%283x-8%29%283x%2B8%29%2F%28x%2B4%29%28x%2B3%29%29\"\"%22%22%2A%22%22\"\"%28%28x%2B3%29%28x%2B3%29%2F%28x%2B3%29%283x%2B8%29%29\"\r\n" );
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document.write( "We cancel the (3x+8)'s\r\n" );
document.write( "\"3x%2B8%3C%3E0%7D%7D%0D%0A%7B%7B%7B3x%3C%3E-8\"\r\n" );
document.write( "\"x%3C%3E-8%2F3\"\r\n" );
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document.write( "We must indicate the restriction that x cannot equal -8/3.\r\n" );
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document.write( "\"%28%283x-8%29%28cross%283x%2B8%29%29%2F%28x%2B4%29%28x%2B3%29%29\"\"%22%22%2A%22%22\"\"%28%28x%2B3%29%28x%2B3%29%2F%28x%2B3%29%28cross%283x%2B8%29%29%29\"\r\n" );
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document.write( "We cancel one of the (x+3)'s and indicate the restriction\r\n" );
document.write( "\"x%2B3%3C%3E0\"\r\n" );
document.write( "\"x%3C%3E-3\"\r\n" );
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document.write( "\"%28%283x-8%29%28cross%283x%2B8%29%29%2F%28x%2B4%29%28cross%28x%2B3%29%29%29\"\"%22%22%2A%22%22\"\"%28%28cross%28x%2B3%29%29%28x%2B3%29%2F%28x%2B3%29%28cross%283x%2B8%29%29%29\"\r\n" );
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document.write( "We cancel the other pair of (x+3)'s.  [We've already indicated this restriction,\r\n" );
document.write( "so we don't need to indicate it again.]\r\n" );
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document.write( "\"%28%283x-8%29%28cross%283x%2B8%29%29%2F%28x%2B4%29%28cross%28x%2B3%29%29%29\"\"%22%22%2A%22%22\"\r\n" );
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document.write( "The final simplification is\r\n" );
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document.write( "\"%283x-8%29%2F%28x%2B4%29\"\r\n" );
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document.write( "We must also indicate that the denominator of the final simplification to\r\n" );
document.write( "prevent it from ever being 0.\r\n" );
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document.write( "\"x%2B4%3C%3E0\"\r\n" );
document.write( "\"x%3C%3E-4\"\r\n" );
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document.write( "So putting in all the restrictions:\r\n" );
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document.write( "Edwin
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