document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825739>Question 825739</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve\r<BR>\n" );
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document.write( "(-3)/(y-4)=(1)/(y+4)\r<BR>\n" );
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document.write( "(w-3)/(w+2)=(6-w)/(w-12)\r<BR>\n" );
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document.write( "Please I need help with this! 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 #497577 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=497577\">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=%28-3%29%2F%28y-4%29=%281%29%2F%28y%2B4%29 ALIGN=MIDDLE  ALT=\"%28-3%29%2F%28y-4%29=%281%29%2F%28y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving equations with fractions is harder than solving equations without fractions. So we will make the problem easier if we eliminate the fractions as soon as possible.<br><BR>\n" );
document.write( "Fractions in an equation can be eliminated by...<ol><li>Find the lowest common denominator (LCD) of all the fractions (on both sides of the equation).</li><li>Multiply both sides of the equation by the LCD.</li></ol>Since the two denominators, (y-4) and (y+4), have no common factors the LCD is simply the product of the two denominators: (y-4)(y+4). So we will multiply both sides by (y-4)(y+4):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-4%29%28y%2B4%29%28%28-3%29%2F%28y-4%29%29=%28y-4%29%28y%2B4%29%28%281%29%2F%28y%2B4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As we multiply, each denominator will cancel with some part of (y-4)(y+4):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%28y-4%29%29%28y%2B4%29%28%28-3%29%2Fcross%28%28y-4%29%29%29=%28y-4%29cross%28%28y%2B4%29%29%28%281%29%2Fcross%28%28y%2B4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B4%29%28-3%29=%28y-4%29%281%29 ALIGN=MIDDLE  ALT=\"%28y%2B4%29%28-3%29=%28y-4%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y-12=y-4 ALIGN=MIDDLE  ALT=\"-3y-12=y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can solve for y. Adding 3y to each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12=4y-4 ALIGN=MIDDLE  ALT=\"-12=4y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding 4 to each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8=4y ALIGN=MIDDLE  ALT=\"-8=4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides by 4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=y ALIGN=MIDDLE  ALT=\"-2=y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Last we check. This is <u>not</u> optional! When both sides of an equation are multiplied by something that might be zero, like (y-4)(y+4), then a check is required. One must make sure that the solution does not make a factor of (y-4)(y+4) equal to zero. A quick visual check should tell us that if y = -2 (our solution) then neither (y-4) nor (y+4) will be a zero. So our solution checks!<br><BR>\n" );
document.write( "I'll leave the second problem up to you to finish. I will just say that the denominators, (w+2) and (w-12), have no common factors between them. So, like the first problem, the LCD is simply their product: (w+2)(w-12)<br><BR>\n" );
document.write( "P.S. This equation has rational expressions. It is not a rational function. It should be posted in the \"polynomials, rational expressions ...\" category. </SPAN>\n" );
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