document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=601853>Question 601853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have  been agonizing over this one for more than an hour already, so I hope someone can explain this to me...\r<BR>\n" );
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document.write( "tan30 + tan45<BR>\n" );
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document.write( "1 - tan30 tan45\r<BR>\n" );
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document.write( "= 1/sqrt3 + 1<BR>\n" );
document.write( " -----------------      ((1))<BR>\n" );
document.write( " 1 - (1/sqrt3)(1)\r<BR>\n" );
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document.write( "= 1 + sqrt3 / sqrt3<BR>\n" );
document.write( "--------------------      ((2))<BR>\n" );
document.write( "sqrt3 - 1 / sqrt3\r<BR>\n" );
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document.write( "= (1 + sqrt3/ sqrt3 - 1) x (sqrt3 + 1/ sqrt3 + 1)     ((3))\r<BR>\n" );
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document.write( "= (1+ sqrt3)(sqrt3 + 1)<BR>\n" );
document.write( " -----------------------        ((4))<BR>\n" );
document.write( "        3-1\r<BR>\n" );
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document.write( "= sqrt3 + 1 + 3 + sqrt3<BR>\n" );
document.write( " -----------------------      ((5))<BR>\n" );
document.write( "          2\r<BR>\n" );
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document.write( "= 4 + 2 sqrt3<BR>\n" );
document.write( "--------------      ((6))<BR>\n" );
document.write( "     2\r<BR>\n" );
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document.write( "= 2(2+ sqrt3)<BR>\n" );
document.write( "--------------       ((7))<BR>\n" );
document.write( "       2\r<BR>\n" );
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document.write( "= 2+sqrt3     ((8))\r<BR>\n" );
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document.write( "My question is, in ((2)), how did 1 become negative? Shouldn't it be 1 - sqrt3 instead of sqrt3 - 1?\r<BR>\n" );
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document.write( "I understand that 1/sqrt3 becomes sqrt3/3 after multiplying it by sqrt3/sqrt3 to get rid of the square root in the decimal, but I really don't get what happened with 1.\r<BR>\n" );
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document.write( "What am I doing wrong? I just can't get to the final answer no matter what I do. Please help me. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380031 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=380031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (tan30 + tan45)<BR>\n" );
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document.write( "(1 - tan30 tan45) \r<BR>\n" );
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document.write( "= (1/sqrt3 + 1)<BR>\n" );
document.write( "----------------- <BR>\n" );
document.write( "(1 - (1/sqrt3)(1)) \r<BR>\n" );
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document.write( "= [(1 + sqrt3) / sqrt3]<BR>\n" );
document.write( "-------------------- <BR>\n" );
document.write( "  [(sqrt(3)-1)]/sqrt(3)]\r<BR>\n" );
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document.write( "====================================\r<BR>\n" );
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document.write( "Invert the denominator and multiply:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [(1 + sqrt3) / sqrt3]<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Cancel the common sqrt(3) to get:<BR>\n" );
document.write( "= [1+sqrt(3)]/[(1-sqrt(3))]<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Multiply numerator and denominator by (1+sqrt(3) to get<BR>\n" );
document.write( "----<BR>\n" );
document.write( "= [1+sqrt(3)]^2 / [1-3]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [1 + 2sqrt(3) + 3]/(-2)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [4 + 2sqrt(3)]/(-2)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "= -2 -sqrt(3)<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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