document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=889756>Question 889756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear tutors, <BR>\n" );
document.write( "It would help me greatly if you could explain to me how to solve these two equations. I already have the answer but I do not know how to get it. So if you could show me the calculation that leads to the asnwer, that would be great. \r<BR>\n" );
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document.write( "Question: 2x^2/ cube root of 4x<BR>\n" );
document.write( "The answer should be = x cube root of 2x^2\r<BR>\n" );
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document.write( "Question: (x/x^2-x-6)-(2/x-3) = 3 \r<BR>\n" );
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document.write( "Thank you so much for you help, \r<BR>\n" );
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document.write( "kate B.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538416 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=538416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. 2x^2 / (4x)^(1/3) =<BR>\n" );
document.write( "multiply both the numerator and denominator by (4x)^(2/3)<BR>\n" );
document.write( "(2x^2) * (4x)^(2/3)) / 4x =<BR>\n" );
document.write( "cancel x and 2 from numerator and denominator<BR>\n" );
document.write( "x * (4x)^(2/3)) / 2 =<BR>\n" );
document.write( "square 4x <BR>\n" );
document.write( "x * (8*2*x^2)^(1/3) / 2 =<BR>\n" );
document.write( "note that cube root of 8 is 2<BR>\n" );
document.write( "2x * (x^2)^(1/3) / 2 =<BR>\n" );
document.write( "cancel 2 from numerator and denominator<BR>\n" );
document.write( "x * (x^2)^(1/3) = x cube root of 2x^2 <BR>\n" );
document.write( "2.  (x/x^2-x-6)-(2/x-3) = 3 <BR>\n" );
document.write( "factor denominator of first fraction<BR>\n" );
document.write( "(x / ((x-3)*(x+2)) - (2/(x-3)) = 3<BR>\n" );
document.write( "common denominator of both fractions is (x-3)*(x+2)<BR>\n" );
document.write( "(x - (2*(x+2)) / ((x-3)*(x+2)) = 3<BR>\n" );
document.write( "expand the numerator<BR>\n" );
document.write( "(x -2x -4) / ((x-3)*(x+2)) = 3<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "(-x -4) = 3*(x-3)*(x+2)<BR>\n" );
document.write( "-x -4 = 3 * (x^2-x-6)<BR>\n" );
document.write( "-x -4 = 3x^2 -3x -18<BR>\n" );
document.write( "3x^2 -2x -14 = 0<BR>\n" );
document.write( "use quadratic formula<BR>\n" );
document.write( "x = (2 + square root((-2)^2 -4*3*(-14)))/(2*3) = 2.519146175 is approx 2.52<BR>\n" );
document.write( "x = (2 - square root((-2)^2 -4*3*(-14)))/(2*3) = &#8722;1.852479508 is approx -1.85<BR>\n" );
document.write( "now check our answers with original equation<BR>\n" );
document.write( "(2.52 / ((2.52)^2 -(2.52) -6) - (2 / ((2.52) / (2.52 - 3))) = 3<BR>\n" );
document.write( "3.005162242 is approx 3<BR>\n" );
document.write( "(-1.85 / ((-1.85)^2 -(-1.85) -6) - (-1.85 / ((-1.85 -3))) = 3<BR>\n" );
document.write( "2.95532646 is approx 3<BR>\n" );
document.write( "our answers of x = 2.52 or -1.85 check with original equation\r<BR>\n" );
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document.write( " </SPAN>\n" );
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