document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206014>Question 206014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3/4=1-3x-2/x+1<BR>\n" );
document.write( "really means 3/4 = 1 - (3x-2)/(x+1) ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156113 by </B><A HREF=/tutors/aboutme.mpl?userid=mickclns><B>mickclns(59)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mickclns><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=156113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Notice the edited version of your question. PLEASE, ALL QUESTIONERS TAKE NOTE: when a fraction is in vertical form, the horizontal division line acts as a grouping operator -- that means: WHEN YOU CONVERT IT INTO HORIZONTAL FORM YOU ***MUST*** USE PARENTHESES TO HAVE IT CONTINUE TO MEAN THE SAME THING.<BR>\n" );
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document.write( "So, first, the solution to what your question means as written:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F4=1-3x-2%2Fx%2B1+ ALIGN=MIDDLE  ALT=\"+3%2F4=1-3x-2%2Fx%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >     subtract 2 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5%2F4=-3x-2%2Fx+ ALIGN=MIDDLE  ALT=\"+-5%2F4=-3x-2%2Fx+\"   DISABLED_style= \"max-width:90%; height:auto;\" >     multiply both sides by 4x to get rid of the fractions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5x=-12x%5E2-8+ ALIGN=MIDDLE  ALT=\"+-5x=-12x%5E2-8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >      add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2%2B8 ALIGN=MIDDLE  ALT=\"12x%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12x%5E2-5x%2B8+=+0+ ALIGN=MIDDLE  ALT=\"+12x%5E2-5x%2B8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "To see whether this factors, look at the discriminant (what's under the square root in the quadratic formula)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac+=%28-5%29%5E2+-+4%2812%29%288%29+=+25+-+384+=+-359 ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac+=%28-5%29%5E2+-+4%2812%29%288%29+=+25+-+384+=+-359\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Since this number is negative, this quadratic expression is not factorable (the discriminant must be a perfect square for the quadratic to be factorable).<BR>\n" );
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document.write( "Using the quadratic formula, then, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+bx+%2B+c+=+0+ ALIGN=MIDDLE  ALT=\"+ax%5E2+%2B+bx+%2B+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12x%5E2-5x%2B8+=+0+ ALIGN=MIDDLE  ALT=\"+12x%5E2-5x%2B8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  a = 12, b=-5, c = 8 (notice you can only use this when one side is 0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2812%29+%2B-+sqrt%28+-359+%29%29%2F%282%2A%2812%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%2812%29+%2B-+sqrt%28+-359+%29%29%2F%282%2A%2812%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=+x+=+%28-12+%2B-+i%2Asqrt%28+359+%29%29%2F24+ ALIGN=MIDDLE  ALT=\"+x+=+%28-12+%2B-+i%2Asqrt%28+359+%29%29%2F24+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which, since 359 is prime is as simple as it gets.<BR>\n" );
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document.write( "OK, now what the problem was probably intended to be (correct me if I'm wrong, I'm not at all certain):<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4+=+1+-+%283x-2%29%2F%28x%2B1%29+ ALIGN=MIDDLE  ALT=\"3%2F4+=+1+-+%283x-2%29%2F%28x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   To get rid of fractions, multiply both sides by 4(x+1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%28x%2B1%29%283%2F4%29+=+4%28x%2B1%29%281+-+%283x-2%29%2F%28x%2B1%29%29+ ALIGN=MIDDLE  ALT=\"+4%28x%2B1%29%283%2F4%29+=+4%28x%2B1%29%281+-+%283x-2%29%2F%28x%2B1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   quick simplification of each side ( on right side 4(x-1) is multiplied by both terms)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28x%2B1%29+=+4%28x%2B1%29+-+4%283x-2%29+ ALIGN=MIDDLE  ALT=\"+3%28x%2B1%29+=+4%28x%2B1%29+-+4%283x-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    next step of simplification: multiplying out<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+3+=+4x+%2B+4+-+12x+%2B+8%29+ ALIGN=MIDDLE  ALT=\"+3x+%2B+3+=+4x+%2B+4+-+12x+%2B+8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   to get x's and constants on opposite sides, add 8x - 3 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11x+=+9+ ALIGN=MIDDLE  ALT=\"+11x+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9%2F11+ ALIGN=MIDDLE  ALT=\"+x+=+9%2F11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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