document.write( "Question 38361: 
Please show me how to do long division this way!\r\n" );
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document.write( "  x² - 49y²\r\n" );
document.write( "——————————— ÷ (x² - 7xy)\r\n" );
document.write( " 6x² + 42y\r\n" );
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document.write( "Thanks!
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Algebra.Com's Answer #23935 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
Please show me how to do long division this way! \r\n" );
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document.write( "  x² - 49y²\r\n" );
document.write( "——————————— ÷ (x² - 7xy)\r\n" );
document.write( " 6x² + 42y\r\n" );
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document.write( "This isn't long division.  It's simplifying by \r\n" );
document.write( "\"factoring and cancelling\":\r\n" );
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document.write( "  x² - 49y²\r\n" );
document.write( "——————————— ÷ (x² - 7xy)\r\n" );
document.write( " 6x² + 42y\r\n" );
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document.write( "Write the second fraction over 1\r\n" );
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document.write( "  x² - 49y²    x² - 7xy \r\n" );
document.write( "——————————— ÷ ——————————\r\n" );
document.write( " 6x² + 42y        1\r\n" );
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document.write( "Invert the second fraction and change to multiplication:\r\n" );
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document.write( "  x² - 49y²       1\r\n" );
document.write( "——————————— × ——————————\r\n" );
document.write( " 6x² + 42y     x² - 7xy   \r\n" );
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document.write( "Factor the upper left numerator: x² - 49y² = (x - 7y)(x + 7y)\r\n" );
document.write( "Factor the lower left denominator: 6x² + 42y = 6(x² + 7y)\r\n" );
document.write( "Factor the lower right denominator: x² - 7xy = x(x - 7y)\r\n" );
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document.write( " (x - 7y)(x + 7y)         1\r\n" );
document.write( "—————————————————— × ——————————\r\n" );
document.write( "    6(x² + 7y)        x(x - 7y)\r\n" );
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document.write( "Indicate the multiplication of the numerators and \r\n" );
document.write( "the denominators and write as a single fraction:\r\n" );
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document.write( "   (x - 7y)(x + 7y)     \r\n" );
document.write( "——————————————————————\r\n" );
document.write( "  6(x² + 7y)x(x - 7y)\r\n" );
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document.write( "Write the x next to the 6 as it is customary to write\r\n" );
document.write( "shorter factors first:\r\n" );
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document.write( "   (x - 7y)(x + 7y)     \r\n" );
document.write( "——————————————————————\r\n" );
document.write( "  6x(x² + 7y)(x - 7y)\r\n" );
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document.write( "Cancel the (x - 7y)'s\r\n" );
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document.write( "      1\r\n" );
document.write( "   (x - 7y)(x + 7y)     \r\n" );
document.write( "——————————————————————\r\n" );
document.write( "  6x(x² + 7y)(x - 7y)\r\n" );
document.write( "                1\r\n" );
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document.write( "   (x + 7y)     \r\n" );
document.write( "——————————————\r\n" );
document.write( "  6x(x² + 7y)\r\n" );
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document.write( "Caution: Do not try to cancel the remaining parenthetical\r\n" );
document.write( "factors, because they are not exactly alike, since the x is\r\n" );
document.write( "squared in the bottom but not in the top and you cannot cancel\r\n" );
document.write( "terms between numerator and denominator.  So the only thing\r\n" );
document.write( "you can do is erase the parentheses in the top:\r\n" );
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document.write( "    x + 7y     \r\n" );
document.write( "——————————————\r\n" );
document.write( "  6x(x² + 7y)\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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