document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638414>Question 638414</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rational Equations. Solve the equation.\r<BR>\n" );
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document.write( "(2x-9)/(x-7)+x/2=5/(x-7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #402177 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=402177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to solve for x, you will first need to find the LCD of the fractions involved.  Let's look at the denominators:  x - 7, 2, x - 7.  The LCD of these fractions is 2(x - 7).  We will then multiply each fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x+-+7%29 ALIGN=MIDDLE  ALT=\"2%28x+-+7%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=%28%282x-9%29%2A2%28x-7%29%29%2F%28x-7%29%29 ALIGN=MIDDLE  ALT=\"%28%282x-9%29%2A2%28x-7%29%29%2F%28x-7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2A2%28x-7%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2A2%28x-7%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A2%28x-7%29%29%2F%28x-7%29 ALIGN=MIDDLE  ALT=\"%285%2A2%28x-7%29%29%2F%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we can cancel out the same terms from both the numerator and denominator of each fraction, we are left with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282x-9%29%2Bx%28x-7%29=2%2A5 ALIGN=MIDDLE  ALT=\"2%282x-9%29%2Bx%28x-7%29=2%2A5\"   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=4x-18%2Bx%5E2-7x=10 ALIGN=MIDDLE  ALT=\"4x-18%2Bx%5E2-7x=10\"   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%5E2-3x-18=10 ALIGN=MIDDLE  ALT=\"x%5E2-3x-18=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we subtract the 10 on the right side of the equal sign, from both sides, we are left with a quadratic equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x-28=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x-28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's see if we can solve this equation by factoring.  We need to find out if any numbers that will multiply together and produce -28, can be added together to equal -3: 4 x -7= 28 and when we add 4 to -7, we get -3.  So, turning this equation into factors, we get (x - 7)(x + 4) = 0, which means x = 7 and/or x = -4.  Since we are unsure if either or both will work, we will have to substitute  7 and -4 for x in our original equation.  Uh oh.  Look at the first fraction in our equation.  The denominator is x - 7.  If we plug our 7 in for x, our denominator will equal 0.  Denominators cannot equal 0, therefore, we know right away that 7 cannot be one of our solutions.\r<BR>\n" );
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document.write( "Now, let's try -4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28-4%29-9%29%2F%28-4-7%29%2B%28-4%2F2%29=5%2F%28-4-7%29 ALIGN=MIDDLE  ALT=\"%282%28-4%29-9%29%2F%28-4-7%29%2B%28-4%2F2%29=5%2F%28-4-7%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=%28-17%2F-11%29-2=5%2F%28-11%29 ALIGN=MIDDLE  ALT=\"%28-17%2F-11%29-2=5%2F%28-11%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=%2817%2F11%29-2=-%285%2F11%29 ALIGN=MIDDLE  ALT=\"%2817%2F11%29-2=-%285%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The LCD of our remaining fractions is 11, so we would multiply 11 by each of our fractions by 11, which would leave us with the following:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17+-+22+=+-5 ALIGN=MIDDLE  ALT=\"17+-+22+=+-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=-5+=+-5 ALIGN=MIDDLE  ALT=\"-5+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since both sides of the equal sign are the same, we know that -4 is a solution.\r<BR>\n" );
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document.write( "Final Answer: x = -4<BR>\n" );
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