document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919074>Question 919074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If {( x-sqrt24)(sqrt75 + sqrt 50)}/ ( sqrt75 - sqrt50) = 1 , then what is the value of x.  please solve it.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557475 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=557475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "your solution is shown below.<BR>\n" );
document.write( "the solution is that x = 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 1 shows the original problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 2 multiplies both sides of the equation by (sqrt(75) - sqrt(50)).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 3 divides both sides of the equation by (sqrt(75) + sqrt(50)).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 4 multiplies numerator and denominator of the expression on the right by (sqrt(75 - sqrt(50).<BR>\n" );
document.write( "this rationalizes the denominator and allows further simplification of the problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 5 performs the multiplications indicated.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 6 simplifies the results from step 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 7 simplifies the results even further by simplifying the radicals to get sqrt(75) = 5*sqrt(3) and sqrt(50) = 5*sqrt(2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 8 simplifies the results even further by combining like terms and translating sqrt(3) * sqrt(2) into sqrt(6).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 9 simplifies the results even further by performing by dividing (125 - 50*sqrt(6) by 25.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 10 adds sqrt(24) to both sides of the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 11 simplifies sqrt(24) to make it equal to 2*sqrt(6)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "step 12 combines like terms to make -2*sqrt(6) and +2*sqr5(6) = 0 and therefore cancel out to get the result of x = 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it has been confirmed through the use of my calculator that the solution is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/1101_0001.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/1101_0002.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );