document.write( "Question 89827: Hi, good afternoon.
\n" ); document.write( "Can you please help me with these two problems.
\n" ); document.write( "I do not seem to understand how to:
\n" ); document.write( "Divide and simplify: $\"%283x%5E2%2B13x%2B4%29%2F%2816-x%5E2%29\"$ ÷ $\"%283x%5E2-5x-12%29%2F%283x-12%29\"$
\n" ); document.write( "Simplify by rationalizing the denominator:
\n" ); document.write( " $\"%28sqrt%2811%29-sqrt%285%29%29+%2F+%28sqrt%2811%29%2Bsqrt%285%29%29\"$
\n" ); document.write( "Thank you so much,
\n" ); document.write( "Chocolatechrrys \n" ); document.write( "

Algebra.Com's Answer #65219 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Hi, good afternoon. \r\n" );
document.write( "Can you please help me with these two problems.\r\n" );
document.write( "I do not seem to understand how to: \r\n" );
document.write( "Divide and simplify: ÷ \r\n" );
document.write( "Simplify by rationalizing the denominator: \r\n" );
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document.write( "Thank you so much,\r\n" );
document.write( "Chocolatechrrys \r\n" );
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document.write( "÷ \r\n" );
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document.write( "Let's get each polynomial in order of descending powers of x.\r\n" );
document.write( "Only one isn't, namely . So write the  \r\n" );
document.write( "in order of descending powers of x,  that is, \r\n" );
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document.write( "Now factor -1 out of that \r\n" );
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document.write( "÷ \r\n" );
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document.write( "We can erase the -1 and put a negative sign in front of the\r\n" );
document.write( "first fraction\r\n" );
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document.write( "÷ \r\n" );
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document.write( "Factor everything:\r\n" );
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document.write( "÷ \r\n" );
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document.write( "Invert the second fraction and change the ÷ to multiplication\r\n" );
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document.write( "Indicate the multiplication of the numerators and denominator\r\n" );
document.write( "all as one fraction:\r\n" );
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document.write( "The 's will cancel, and also the 's\r\n" );
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document.write( "So we end up with\r\n" );
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document.write( "You can leave that just asit is, or if you like,\r\n" );
document.write( "you can multiply the numerator and denominator out:\r\n" );
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document.write( "As you see, we could have gotten by without\r\n" );
document.write( "factoring the  but we had no way\r\n" );
document.write( "or knowing in advance that neither of its factors\r\n" );
document.write( "would cancel, and they might have.\r\n" );
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document.write( "Put parentheses around the top and bottom:\r\n" );
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document.write( "Form the conjugate of the denominator by\r\n" );
document.write( "copying it over and changing the sign of\r\n" );
document.write( "only the second term.  So the conjugate\r\n" );
document.write( "of denominator  is\r\n" );
document.write( ". Now multiply by the \r\n" );
document.write( "fraction \r\n" );
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document.write( ", which just equals 1.\r\n" );
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document.write( "·\r\n" );
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document.write( "Indicating the multiplication of numerators and \r\n" );
document.write( "denominators:\r\n" );
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document.write( "Now use FOIL to multiply out:\r\n" );
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document.write( "Multiplying under the radicals\r\n" );
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document.write( "The two middle terms in the top combine as ,\r\n" );
document.write( "and the two middle terms cancel in the bottom:\r\n" );
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document.write( "Combining the numbers \r\n" );
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document.write( "Factor 2 out of the top:\r\n" );
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document.write( "Cancel the 2 into the 6 and get\r\n" );
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document.write( "Edwin

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