document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=616036>Question 616036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello I need help adding fractions and equations in math<BR>\n" );
document.write( "i need to know how to do 3n +5 over 6 - 10 over n = n over 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387487 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=387487\">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=%283n%2B5%29%2F6-10%2Fn=n%2F2 ALIGN=MIDDLE  ALT=\"%283n%2B5%29%2F6-10%2Fn=n%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "That could be written as (3n+5)/6-10/n=n/2<BR>\n" );
document.write( "(When you cannot write the long horizontal fraction bar, it takes a sets of parenthesis to indicate that (3n+5) would be computed first).<BR>\n" );
document.write( " <BR>\n" );
document.write( "TIP:<BR>\n" );
document.write( "Fractions and denominators give you more chances to make mistakes.<BR>\n" );
document.write( "When solving equations, it is a good idea to get rid of denominators as soon as possible.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Faced with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283n%2B5%29%2F6-10%2Fn=n%2F2 ALIGN=MIDDLE  ALT=\"%283n%2B5%29%2F6-10%2Fn=n%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , to get rid of denominators in one step, I would multiply both sides of the equation times 6n (but see CAUTION below).<BR>\n" );
document.write( "I choose 6n because it is a multiple of all three denominators (6, n, and 2).<BR>\n" );
document.write( "Shown in small steps, it would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283n%2B5%29%2F6-10%2Fn=n%2F2 ALIGN=MIDDLE  ALT=\"%283n%2B5%29%2F6-10%2Fn=n%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6n%28%283n%2B5%29%2F6-10%2Fn%29=6n%28n%2F2%29 ALIGN=MIDDLE  ALT=\"6n%28%283n%2B5%29%2F6-10%2Fn%29=6n%28n%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6n%283n%2B5%29%2F6-6n%2A10%2Fn=6n%2An%2F2 ALIGN=MIDDLE  ALT=\"6n%283n%2B5%29%2F6-6n%2A10%2Fn=6n%2An%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%283n%2B5%29-60=3n%5E2 ALIGN=MIDDLE  ALT=\"n%283n%2B5%29-60=3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2%2B5n-60=3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2%2B5n-60=3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Probably you would not need to show all those steps, and it would be enough to write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283n%2B5%29%2F6-10%2Fn=n%2F2 ALIGN=MIDDLE  ALT=\"%283n%2B5%29%2F6-10%2Fn=n%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2%2B5n-60=3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2%2B5n-60=3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283n%2B5%29%2F6-10%2Fn=n%2F2 ALIGN=MIDDLE  ALT=\"%283n%2B5%29%2F6-10%2Fn=n%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%283n%2B5%29-60=3n%5E2 ALIGN=MIDDLE  ALT=\"n%283n%2B5%29-60=3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2%2B5n-60=3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2%2B5n-60=3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You would continue with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2%2B5n-60=3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2%2B5n-60=3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n-60=0 ALIGN=MIDDLE  ALT=\"5n-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (subtracting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides)<BR>\n" );
document.write( "The final steps could be written many different ways. One options is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n-60=0 ALIGN=MIDDLE  ALT=\"5n-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n=60 ALIGN=MIDDLE  ALT=\"5n=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=60%2F5 ALIGN=MIDDLE  ALT=\"n=60%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=12%29 ALIGN=MIDDLE  ALT=\"highlight%28n=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "CAUTION:<BR>\n" );
document.write( "When you have a variable in a denominator and proceed as done above, multiplying times an expression that involves a variable (like 6n), new solutions may creep into your transformed equation. Those solutions of the final equation that are not solutions of the original equation are called extraneous solutions. You get rid of any extraneous solution that could pop up when you verify your solutions.<BR>\n" );
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document.write( "VERIFYING THE SOLUTION:<BR>\n" );
document.write( "Verifying helps to find out mistakes and extraneous solutions too.<BR>\n" );
document.write( "Substituting solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=12 ALIGN=MIDDLE  ALT=\"n=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283n%2B5%29%2F6-10%2Fn=n%2F2 ALIGN=MIDDLE  ALT=\"%283n%2B5%29%2F6-10%2Fn=n%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A12%2B5%29%2F6-10%2F12=12%2F2 ALIGN=MIDDLE  ALT=\"%283%2A12%2B5%29%2F6-10%2F12=12%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836%2B5%29%2F6-5%2F6=6 ALIGN=MIDDLE  ALT=\"%2836%2B5%29%2F6-5%2F6=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836%2B5-5%29%2F6=6 ALIGN=MIDDLE  ALT=\"%2836%2B5-5%29%2F6=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F6=6 ALIGN=MIDDLE  ALT=\"36%2F6=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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