document.write( "Question 188648: . Rationalize the denominator:
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\n" ); document.write( " √[6] – √[5]
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\n" ); document.write( "2/sqrt[6]-[5]\r
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\n" ); document.write( "\n" ); document.write( ". Simplify the rational expression:
\n" ); document.write( "x2 – 3x – 10 find the gcf of the polynomial
\n" ); document.write( " x2 – x – 20\r
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\n" ); document.write( "\n" ); document.write( ". Simplify:
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Algebra.Com's Answer #141444 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
# 1\r
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\n" ); document.write( "\n" ); document.write( "\"2%2F%28+sqrt%286%29-sqrt%285%29+%29+\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " Multiply both the numerator and denominator by \"sqrt%286%29%2Bsqrt%285%29\" (the conjugate of the denominator). This will rationalize the denominator\r
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\n" ); document.write( "\n" ); document.write( " FOIL\r
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\n" ); document.write( "\n" ); document.write( "\"%282%28+sqrt%286%29%2Bsqrt%285%29+%29%29%2F%28+6-5+%29\" Square each term.\r
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\n" ); document.write( "\n" ); document.write( "\"%282%28+sqrt%286%29%2Bsqrt%285%29+%29%29%2F%28+1+%29\" Subtract\r
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\n" ); document.write( "\n" ); document.write( "\"2%28+sqrt%286%29%2Bsqrt%285%29+%29\" Reduce\r
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\n" ); document.write( "\n" ); document.write( "\"2%2Asqrt%286%29%2B2%2Asqrt%285%29\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "So \"2%2F%28+sqrt%286%29-sqrt%285%29+%29+=+2%2Asqrt%286%29%2B2%2Asqrt%285%29+\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%5E2-3x-10%29%2F%28x%5E2-x-20%29\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "\"%28%28x%2B2%29%2A%28x-5%29%29%2F%28x%5E2-x-20%29\" Factor \"x%5E2-3x-10\" to get \"%28x%2B2%29%2A%28x-5%29\".\r
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\n" ); document.write( "\n" ); document.write( "\"%28%28x%2B2%29%2A%28x-5%29%29%2F%28%28x%2B4%29%2A%28x-5%29%29\" Factor \"x%5E2-x-20\" to get \"%28x%2B4%29%2A%28x-5%29\".\r
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\n" ); document.write( "\n" ); document.write( "\"%28%28x%2B2%29highlight%28%28x-5%29%29%29%2F%28%28x%2B4%29highlight%28%28x-5%29%29%29\" Highlight the common terms. \r
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\n" ); document.write( "\n" ); document.write( "\"%28%28x%2B2%29cross%28%28x-5%29%29%29%2F%28%28x%2B4%29cross%28%28x-5%29%29%29\" Cancel out the common terms. Note: the GCF is \"x-5\" and is canceled out.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B2%29%2F%28x%2B4%29\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So \"%28x%5E2-3x-10%29%2F%28x%5E2-x-20%29\" simplifies to \"%28x%2B2%29%2F%28x%2B4%29\".\r
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\n" ); document.write( "\n" ); document.write( "In other words, \"%28x%5E2-3x-10%29%2F%28x%5E2-x-20%29=%28x%2B2%29%2F%28x%2B4%29\" where \"x%3C%3E-4\" or \"x%3C%3E5\"\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%28144%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E12%2Az%5E18%29\" Factor \"x%5E10\" into \"x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2\"\r
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\n" ); document.write( "\n" ); document.write( " Factor \"y%5E12\" into \"y%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2\"\r
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\n" ); document.write( "\n" ); document.write( " Factor \"z%5E18\" into \"z%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2\"\r
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\n" ); document.write( "\n" ); document.write( " Break up the square root using the identity \"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29\".\r
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\n" ); document.write( "\n" ); document.write( " Take the square root of \"144\" to get \"12\".\r
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\n" ); document.write( "\n" ); document.write( " Take the square root of \"x%5E2\" to get \"x\".\r
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\n" ); document.write( "\n" ); document.write( " Take the square root of \"y%5E2\" to get \"y\".\r
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\n" ); document.write( "\n" ); document.write( "\"12%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az\" Take the square root of \"z%5E2\" to get \"z\".\r
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\n" ); document.write( "\n" ); document.write( "\"12x%5E5y%5E6z%5E9\" Rearrange and multiply the terms.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So \"sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29\" simplifies to \"12x%5E5y%5E6z%5E9\"\r
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\n" ); document.write( "\n" ); document.write( "In other words, \"sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29=12x%5E5y%5E6z%5E9\" where every variable is non-negative. \n" ); document.write( "
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