document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160798>Question 1160798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the variable x, write a rational expression that would have the given restrictions. <BR>\n" );
document.write( "X≠0, x≠ ±3/4\r<BR>\n" );
document.write( "\n" );
document.write( "What would the denomainator of the rational expression 7x-13/(4-3x) have to be multiplied by to end up with a denominator in the rational expressions of 20x^(2)-15x^(3)?\r<BR>\n" );
document.write( "\n" );
document.write( "If the rational expression 4x^(2)-2x/4x^(2)+20x can be simplified to 2x-1/2x+10 what are the restrictions on the original rational expression? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784192 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=784192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-13%29%2F%284-3x%29 ALIGN=MIDDLE  ALT=\"%287x-13%29%2F%284-3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > have to be multiplied by to end up with a denominator in the rational expressions of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E2-15x%5E3 ALIGN=MIDDLE  ALT=\"20x%5E2-15x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E2-15x%5E3 ALIGN=MIDDLE  ALT=\"20x%5E2-15x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%284-3x%29 ALIGN=MIDDLE  ALT=\"5x%5E2%284-3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-13%29%2F%284-3x%29 ALIGN=MIDDLE  ALT=\"%287x-13%29%2F%284-3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > have to be multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2 ALIGN=MIDDLE  ALT=\"5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "If the rational expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-2x%29%2F%284x%5E2%2B20x%29+ ALIGN=MIDDLE  ALT=\"%284x%5E2-2x%29%2F%284x%5E2%2B20x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%2F%282x%2B10%29 ALIGN=MIDDLE  ALT=\"%282x-1%29%2F%282x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > what are the restrictions on the original rational expression?\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-2x%29%2F%284x%5E2%2B20x%29+ ALIGN=MIDDLE  ALT=\"%284x%5E2-2x%29%2F%284x%5E2%2B20x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >......in both numerator and denominator factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%282x-1%29%2F2x%282x%2B10%29+ ALIGN=MIDDLE  ALT=\"2x%282x-1%29%2F2x%282x%2B10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........simplify\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%282x%29%282x-1%29%2Fcross%282x%29%282x%2B10%29+ ALIGN=MIDDLE  ALT=\"cross%282x%29%282x-1%29%2Fcross%282x%29%282x%2B10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, both numerator and denominator  the rational expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-2x%29%2F%284x%5E2%2B20x%29+ ALIGN=MIDDLE  ALT=\"%284x%5E2-2x%29%2F%284x%5E2%2B20x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor out common <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to simplify to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282x-1%29%2F%282x%2B10%29 ALIGN=MIDDLE  ALT=\"+%282x-1%29%2F%282x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );