document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201760>Question 201760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5x-2/3x-3 - x/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 #152004 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=152004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to combine these terms, because fractions are involved, we need common denominators. And it is to our advantage to use the Lowest Common Denominator (LCD).<br><BR>\n" );
document.write( "First let's rewrite the first term as a fraction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%29%2F1+-+2%2F%283x-3%29+-+x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%285x%29%2F1+-+2%2F%283x-3%29+-+x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the LCD we need to factor all the denominators. Only the middle denominator will factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%29%2F1+-+2%2F%283%28x-1%29%29+-+x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%285x%29%2F1+-+2%2F%283%28x-1%29%29+-+x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The LCD will be the product of all the different factors of all the denominators. So our LCD will be: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%2A%28x-1%29 ALIGN=MIDDLE  ALT=\"%283%29%2A%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. To change the denominators into the LCD we will multiply the numerator and denominator of each fraction by the factors of the LCD it is \"missing\", if any. The first fraction is missing both factors, the second factor is not missing any factors and the third fraction is missing the factor of 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285x%29%2F1%29%2A%28%28%283%29%2A%28x-1%29%29%2F%28%283%29%2A%28x-1%29%29%29+-+2%2F%283x-3%29+-+%28x%2F%28x-1%29%29%2A%283%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply the numerators (but leave the denominators in factored form):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x%5E2+-+15x%29%2F%28%283%29%2A%28x-1%29%29+-+2%2F%28%283%29%2A%28x-1%29%29+-+%283x%29%2F%28%283%29%2A%28x-1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can combine the terms since the denominators are the same:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x%5E2+-+18x+-+2%29%2F%28%283%29%2A%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%2815x%5E2+-+18x+-+2%29%2F%28%283%29%2A%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is our answer. But as with all answers that are fractions, we should try to reduce the fraction be canceling common factors. (This is why we left the denominators factored earlier.) But the numerator does not factor. So this fraction cannot be reduced. So now we can go ahead and multiply out the denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x%5E2+-+18x+-+2%29%2F%283x+-+3%29 ALIGN=MIDDLE  ALT=\"%2815x%5E2+-+18x+-+2%29%2F%283x+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );