document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76648>Question 76648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you teach me how to do a rational equation and check it?\r<BR>\n" );
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document.write( "x/6-x/8=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54968 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F6%29-%28x%2F8%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%2F6%29-%28x%2F8%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can get rid of both denominators by multiplying all the terms on both sides of the equation<BR>\n" );
document.write( "by one of two methods. You can either first multiply the entire equation first by 6 and next<BR>\n" );
document.write( "by 8 or you can multiply the entire equation by 48, the product of 6*8.<BR>\n" );
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document.write( "Let's do it in two stages.  First multiply by 6 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Ax%2F6%29+-+%286%2Ax%2F8%29+=+6%2A1 ALIGN=MIDDLE  ALT=\"%286%2Ax%2F6%29+-+%286%2Ax%2F8%29+=+6%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then multiply this equation by 8 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2A6%2Ax%2F6%29+-+%288%2A6%2Ax%2F8%29+=+8%2A6%2A1 ALIGN=MIDDLE  ALT=\"%288%2A6%2Ax%2F6%29+-+%288%2A6%2Ax%2F8%29+=+8%2A6%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "At this point you are at the same place that you would have been if you had just multiplied<BR>\n" );
document.write( "the entire equation by 48 ... the product of the denominators.<BR>\n" );
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document.write( "Now, where you have the same term in the denominator and the numerator, you can cancel them<BR>\n" );
document.write( "out as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Across%286%29%2Ax%2Fcross%286%29+-+cross%288%29%2A6%2Ax%2Fcross%288%29+=+8%2A6%2A1 ALIGN=MIDDLE  ALT=\"8%2Across%286%29%2Ax%2Fcross%286%29+-+cross%288%29%2A6%2Ax%2Fcross%288%29+=+8%2A6%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This leaves you with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2Ax%29+-+6%2Ax+=+48 ALIGN=MIDDLE  ALT=\"%288%2Ax%29+-+6%2Ax+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that I multiplied out the right side.  Now you can combine the two terms on the<BR>\n" );
document.write( "left side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+48 ALIGN=MIDDLE  ALT=\"2x+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this can be solved by dividing both the left and right side by 2 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+48%2F2+=+24 ALIGN=MIDDLE  ALT=\"x+=+48%2F2+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Check this by going back to the original problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F6%29-%28x%2F8%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%2F6%29-%28x%2F8%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now substitute 24 for x and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824%2F6%29-%2824%2F8%29+=+1 ALIGN=MIDDLE  ALT=\"%2824%2F6%29-%2824%2F8%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But 24 divided by 6 is 4 and 24 divided by 8 is 3.  Substitute these values and the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+-+3+=+1 ALIGN=MIDDLE  ALT=\"4+-+3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And obviously the left side equals the right side.  So our answer of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24 ALIGN=MIDDLE  ALT=\"x+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" > is correct.<BR>\n" );
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document.write( "You can use this method to get rid of the denominators, and then you are working with an<BR>\n" );
document.write( "ordinary old algebraic equation ... which is a lot easier than trying to mess around with<BR>\n" );
document.write( "fractions.  Hope this helps you to understand a method of solving an equation like this<BR>\n" );
document.write( "one. </SPAN>\n" );
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