document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=846547>Question 846547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I AM STUCK WITH THIS ONE AND IT IS MOST OFTEN ASKED SO PLEASE HELP ME !! 2 ( x-1 / x+3 ) -7 ( x+3 / x-1 ) = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509825 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=509825\">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=2%28%28x-1%29%2F%28x%2B3%29%29-7%28%28x%2B3%29%2F%28x-1%29%29=5 ALIGN=MIDDLE  ALT=\"2%28%28x-1%29%2F%28x%2B3%29%29-7%28%28x%2B3%29%2F%28x-1%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first thing we need to do is multiply 2 by (x - 1) and multiply 7 by (x + 3):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x-2%29%2F%28x%2B3%29%29-%28%287x%2B21%29%2F%28x-1%29%29=5 ALIGN=MIDDLE  ALT=\"%28%282x-2%29%2F%28x%2B3%29%29-%28%287x%2B21%29%2F%28x-1%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, we need to subtract the remaining fractions on the left side of the equation.  We do this by multiplying (2x - 2) by (x - 1) and multiplying (7x + 21) by (x + 3) and setting this result in the numerator and setting (x + 3)(x - 1) in the denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%282x-2%29%2A%28x-1%29%29%2F%28%28x%2B3%29%2A%28x-1%29%29%29-%28%28%287x%2B21%29%2A%28x%2B3%29%29%2F%28%28x%2B3%29%2A%28x-1%29%29%29=5 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=%28%28%282x%5E2-4x%2B2%29%29%2F%28%28x%2B3%29%2A%28x-1%29%29-%28%287x%5E2%2B42x%2B63%29%29%2F%28%28x%2B3%29%2A%28x-1%29%29%29=5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, after distributing the minus sign to (7x^2 + 42x + 63), combine all of the terms in the numerator and set that above the denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2-4x%2B2-7x%5E2-42x-63%29%2F%28%28x%2B3%29%28x-1%29%29=5 ALIGN=MIDDLE  ALT=\"%282x%5E2-4x%2B2-7x%5E2-42x-63%29%2F%28%28x%2B3%29%28x-1%29%29=5\"   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=%28-5x%5E2-46x-61%29%2F%28%28x%2B3%29%28x-1%29%29=5 ALIGN=MIDDLE  ALT=\"%28-5x%5E2-46x-61%29%2F%28%28x%2B3%29%28x-1%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, since this single fraction is set equal to a number, we will cross-multiply the numerator in the fraction, by 1, since 5 = 5/1, and multiply the denominator in the fraction by 5:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%5E2-46x-61=5%28x%2B3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"-5x%5E2-46x-61=5%28x%2B3%29%28x-1%29\"   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=-5x%5E2-46x-61=5%28x%5E2%2B2x-3%29 ALIGN=MIDDLE  ALT=\"-5x%5E2-46x-61=5%28x%5E2%2B2x-3%29\"   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=-5x%5E2-46x-61=5x%5E2%2B10x-15 ALIGN=MIDDLE  ALT=\"-5x%5E2-46x-61=5x%5E2%2B10x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, since this is a quadratic equation, we need to move all of the terms to one side of the equation and set the other side of the equation equal to 0:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=5x%5E2%2B5x%5E2%2B10x%2B46x-15%2B61 ALIGN=MIDDLE  ALT=\"0=5x%5E2%2B5x%5E2%2B10x%2B46x-15%2B61\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Combining like terms gives us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=10x%5E2%2B56x%2B46 ALIGN=MIDDLE  ALT=\"0=10x%5E2%2B56x%2B46\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have this in quadratic form.  Let's make this equation easier to factor by factoring out 2, giving us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2%285x%5E2%2B28x%2B23%29 ALIGN=MIDDLE  ALT=\"0=2%285x%5E2%2B28x%2B23%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, this is easily factorable:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2%285x%2B23%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"0=2%285x%2B23%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can discard the 2 we factored out, and set each of our factors equal to zero to find our x's:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B23=0 ALIGN=MIDDLE  ALT=\"5x%2B23=0\"   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=5x=-23 ALIGN=MIDDLE  ALT=\"5x=-23\"   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=x=-23%2F5 ALIGN=MIDDLE  ALT=\"x=-23%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "AND\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   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=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We now have solved for x.\r<BR>\n" );
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document.write( "x = -1 and -23/5\r<BR>\n" );
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document.write( "You need to verify both of these values of x work by plugging each value of x into the original equation.  Both, in fact, do work, so\r<BR>\n" );
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document.write( "x = -1 and -23/5\r<BR>\n" );
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document.write( " </SPAN>\n" );
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