document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462560>Question 462560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the following rational expression: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28x%2B1%29%2B2%2F%283x%29 ALIGN=MIDDLE  ALT=\"3%2F%28x%2B1%29%2B2%2F%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317104 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify the following rational expression: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28x%2B1%29%2B2%2F%283x%29 ALIGN=MIDDLE  ALT=\"3%2F%28x%2B1%29%2B2%2F%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that I changed the wording of your question. You have given us an algebraic expression (with no equal sign.) In an expression, there is nothing to SOLVE. The variable x can be almost any number.However, we can SIMPLIFY this expression into a single term.<BR>\n" );
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document.write( "This might seem like a picky thing, but in the language of mathematics, words are very important. It's best to be a precise as you can!<BR>\n" );
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document.write( "So, let's simplify this thing! We have an expression with two terms; both are fractions. In order to add them, we need a common denominator (just like you did when you added fractions in elementary school.)<BR>\n" );
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document.write( "An easy way to get a common denominator, it to multiply each term by the other term's denominator over itself. In other words, I multiply the first term by (3x)/(3x) and the second term by (x+1)/(/(x+1).I can do this because I'm really multiplying by a fancy version of one. (any number divided by itself equals one.) Watch what happens:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F%28x%2B1%29%29%2A%28%283x%29%2F%283x%29%29%2B%282%2F%283x%29%29%2A%28%28x%2B1%29%2F%28x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now both terms have the same denominator, so we can add them together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%283%29%283x%29%29%2F%28%28x%2B1%29%283x%29%29%29%2B%28%28%282%29%28x%2B1%29%29%2F%28%28x%2B1%29%283x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%29%283x%29%2B%282%29%28x%2B1%29%29%2F%28%28x%2B1%29%283x%29%29 ALIGN=MIDDLE  ALT=\"%28%283%29%283x%29%2B%282%29%28x%2B1%29%29%2F%28%28x%2B1%29%283x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can distribute the 3 and 2 over their parentheses in the numerator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%2B2x%2B2%29%2F%28%28x%2B1%29%283x%29%29 ALIGN=MIDDLE  ALT=\"%289x%2B2x%2B2%29%2F%28%28x%2B1%29%283x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can combine like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2811x%2B2%29%2F%28%28x%2B1%29%283x%29%29 ALIGN=MIDDLE  ALT=\"+%2811x%2B2%29%2F%28%28x%2B1%29%283x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, we use the distributive property to simplify the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2811x%2B2%29%2F%283x%5E2%2B3x%29 ALIGN=MIDDLE  ALT=\"+%2811x%2B2%29%2F%283x%5E2%2B3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "hope this helps!<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex </SPAN>\n" );
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