document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95951>Question 95951</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618052917/algebrahomeworkh>Precalculus with limits</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation: (7/(2x+1))-(8x/(2x-1))=-4<BR>\n" );
document.write( "I'm really bad at the equations with fractions! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69890 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=69890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to solve:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F%282x%2B1%29%29-%288x%2F%282x-1%29%29=-4 ALIGN=MIDDLE  ALT=\"%287%2F%282x%2B1%29%29-%288x%2F%282x-1%29%29=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you don't like fractions, in this case you can get rid of the fractions. How? Begin by noting<BR>\n" );
document.write( "that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%282x-1%29 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a common denominator. Suppose that we multiply both sides of this<BR>\n" );
document.write( "equation (all terms) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%282x-1%29 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In doing that multiplication you make the original<BR>\n" );
document.write( "problem become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%2B1%29%282x-1%29%2A7%29%2F%282x%2B1%29+-%28%282x%2B1%29%282x-1%29%2A8x%29%2F%282x-1%29+=+-4%2A%282x%2B1%29%282x-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, where it applies you can cancel the denominator with the like term in the numerator as<BR>\n" );
document.write( "follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cross%282x%2B1%29%29%2A%282x-1%29%2A7%29%2F%28cross%282x%2B1%29%29+-%28%282x%2B1%29%28cross%282x-1%29%29%2A8x%29%2F%28cross%282x-1%29%29+=+-4%2A%282x%2B1%29%282x-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "After these cancellations you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x+-1%29%2A7%29+-+%28%282x%2B1%29%2A8x%29+=+-4%2A%282x%2B1%29%282x-1%29 ALIGN=MIDDLE  ALT=\"%28%282x+-1%29%2A7%29+-+%28%282x%2B1%29%2A8x%29+=+-4%2A%282x%2B1%29%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+1%29%2A7 ALIGN=MIDDLE  ALT=\"%282x+-+1%29%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x+-+7 ALIGN=MIDDLE  ALT=\"14x+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+1%29%2A8x ALIGN=MIDDLE  ALT=\"%282x+%2B+1%29%2A8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+%2B+8x ALIGN=MIDDLE  ALT=\"16x%5E2+%2B+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and finally, <BR>\n" );
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document.write( "Multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A%282x%2B1%29%282x+-1%29 ALIGN=MIDDLE  ALT=\"-4%2A%282x%2B1%29%282x+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2+%2B+4 ALIGN=MIDDLE  ALT=\"-16x%5E2+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute these results into the equation and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x+-+7+-+%2816x%5E2+%2B+8x%29+=+-16x%5E2+%2B+4 ALIGN=MIDDLE  ALT=\"14x+-+7+-+%2816x%5E2+%2B+8x%29+=+-16x%5E2+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side you can remove the parentheses if you change the signs of the terms inside<BR>\n" );
document.write( "the parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x+-+7+-+16x%5E2+-+8x+=+-16x%5E2+%2B+4 ALIGN=MIDDLE  ALT=\"14x+-+7+-+16x%5E2+-+8x+=+-16x%5E2+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2 ALIGN=MIDDLE  ALT=\"-16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > on both sides. Therefore, if you add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2 ALIGN=MIDDLE  ALT=\"16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<BR>\n" );
document.write( "both sides these two terms disappear and you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x+-+7+-+8x+=+4 ALIGN=MIDDLE  ALT=\"14x+-+7+-+8x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side you can combine the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x ALIGN=MIDDLE  ALT=\"14x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x ALIGN=MIDDLE  ALT=\"-8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to reduce<BR>\n" );
document.write( "the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+-+7+=+4 ALIGN=MIDDLE  ALT=\"6x+-+7+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then get rid of the -7 on the left side by adding 7 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+11 ALIGN=MIDDLE  ALT=\"6x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, solve for x by dividing both sides by 6 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11%2F6 ALIGN=MIDDLE  ALT=\"x+=+11%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the answer you are looking for ... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11%2F6 ALIGN=MIDDLE  ALT=\"x+=+11%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can check this answer by substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F6 ALIGN=MIDDLE  ALT=\"11%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > for x in the original problem and<BR>\n" );
document.write( "ensuring that the equation will balance. <BR>\n" );
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document.write( "Hope this helps you to understand the problem and how you can get rid of the denominators in<BR>\n" );
document.write( "the equation so that you are not working with fractions.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );