document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74431>Question 74431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I need help with adding and subtracting with unlike denominators. If you can do these 3 problems and try to explain how you did them I would be very appreicative. \r<BR>\n" );
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document.write( "1.  (x+8)/(3x-1) + (x+3)/(x+1)<BR>\n" );
document.write( "2.  4/(x+4) - 7/5x<BR>\n" );
document.write( "3.  4x/(5x-2) - 2x/(5x+1)\r<BR>\n" );
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document.write( "Thank You!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53431 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=53431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When we add fractions with different denominators we have to make them the same so we can add them. For instance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2B1%2F3 ALIGN=MIDDLE  ALT=\"1%2F2%2B1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be added unless we have similar denominators. To make them have like denominators, we have to find a common number that they can multiply to. 2 and 3 can both multiply to 6 (for instance 2*3=6 and 3*2=6). Since they're both at 6 we can now add them. In other words this happens\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2B1%2F3=%283%2F3%29%281%2F2%29%2B%282%2F2%29%281%2F3%29=3%2F6%2B2%2F6=%283%2B2%29%2F6=5%2F6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Notice how we multiplied each term by a form of 1 (2/2 and 3/3) so they didn't change. So to find the common denominator we multiply the 2 denominators.<BR>\n" );
document.write( "This same idea applies to unknown variables. \r<BR>\n" );
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document.write( "1.<BR>\n" );
document.write( "The common denominator is:<BR>\n" );
document.write( "(x+1)(3x-1) we can leave it as it is. We don't need to foil.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29%2F%283x-1%29+%2B+%28x%2B3%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B8%29%2F%283x-1%29+%2B+%28x%2B3%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%2F%28x%2B1%29%29%28%28x%2B8%29%2F%283x-1%29%29+%2B+%28%283x-1%29%2F%283x-1%29%29%28%28x%2B3%29%2F%28x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Multiply the first term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a clever form of 1 to get to the common denominator. Multiply the second term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-1%29%2F%283x-1%29 ALIGN=MIDDLE  ALT=\"%283x-1%29%2F%283x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a clever form of 1 to get to the common denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%28x%2B8%29%29%2F%28%28x%2B1%29%283x-1%29%29%2B%28%283x-1%29%28x%2B3%29%29%2F%28%28x%2B1%29%283x-1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Since they have similar denominators, we can add now.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%28x%2B8%29%2B%283x-1%29%28x%2B3%29%29%2F%28%28x%2B1%29%283x-1%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%28x%2B8%29%2B%283x-1%29%28x%2B3%29%29%2F%28%28x%2B1%29%283x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B9x%2B8%2B3x%5E2%2B8x-3%29%2F%28%28x%2B1%29%283x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B9x%2B8%2B3x%5E2%2B8x-3%29%2F%28%28x%2B1%29%283x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >which foils to this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2%2B17x%2B5%29%2F%28%28x%2B1%29%283x-1%29%29 ALIGN=MIDDLE  ALT=\"%284x%5E2%2B17x%2B5%29%2F%28%28x%2B1%29%283x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Which simplifies to this\r<BR>\n" );
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document.write( "2.The common denominator is (5x)(x+4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28x%2B4%29+-+7%2F5x ALIGN=MIDDLE  ALT=\"4%2F%28x%2B4%29+-+7%2F5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2F5x%29%284%2F%28x%2B4%29%29+-+%28%28x%2B4%29%2F%28x%2B4%29%29%287%2F5x%29 ALIGN=MIDDLE  ALT=\"%285x%2F5x%29%284%2F%28x%2B4%29%29+-+%28%28x%2B4%29%2F%28x%2B4%29%29%287%2F5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Multiply the first term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%29%2F%285x%29 ALIGN=MIDDLE  ALT=\"%285x%29%2F%285x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a clever form of 1 to get to the common denominator. Multiply the second term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a clever form of 1 to get to the common denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%2F%285x%28x%2B4%29%29+-+%287%28x%2B4%29%29%2F%285x%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"20x%2F%285x%28x%2B4%29%29+-+%287%28x%2B4%29%29%2F%285x%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x-7%28x%2B4%29%29%2F%285x%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%2820x-7%28x%2B4%29%29%2F%285x%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x-7x-28%29%2F%285x%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%2820x-7x-28%29%2F%285x%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Distribute the 7 to each term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813x-28%29%2F%285x%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%2813x-28%29%2F%285x%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify\r<BR>\n" );
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document.write( "3.The common denominator is (5x-2)(5x+1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F%285x-2%29+-+2x%2F%285x%2B1%29 ALIGN=MIDDLE  ALT=\"4x%2F%285x-2%29+-+2x%2F%285x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285x%2B1%29%2F%285x%2B1%29%29%284x%2F%285x-2%29%29+-+%28%285x-2%29%2F%285x-2%29%29%282x%2F%285x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Multiply the first term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B1%29%2F%285x%2B1%29 ALIGN=MIDDLE  ALT=\"%285x%2B1%29%2F%285x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a clever form of 1 to get to the common denominator. Multiply the second term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-2%29%2F%285x-2%29 ALIGN=MIDDLE  ALT=\"%285x-2%29%2F%285x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a clever form of 1 to get to the common denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%285x%2B1%29%29%2F%28%285x%2B1%29%285x-2%29%29+-+%282x%285x-2%29%29%2F%28%285x%2B1%29%285x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%285x%2B1%29-2x%285x-2%29%29%2F%28%285x%2B1%29%285x-2%29%29 ALIGN=MIDDLE  ALT=\"%284x%285x%2B1%29-2x%285x-2%29%29%2F%28%285x%2B1%29%285x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x%5E2%2B4x-10x%5E2%2B4x%29%2F%28%285x%2B1%29%285x-2%29%29 ALIGN=MIDDLE  ALT=\"%2820x%5E2%2B4x-10x%5E2%2B4x%29%2F%28%285x%2B1%29%285x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Distribute<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x%5E2%2B8x%29%2F%28%285x%2B1%29%285x-2%29%29 ALIGN=MIDDLE  ALT=\"%2810x%5E2%2B8x%29%2F%28%285x%2B1%29%285x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify\r<BR>\n" );
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document.write( "Hope this helps. </SPAN>\n" );
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