document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388707>Question 388707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve (2x-5)/(x)+(4x-1)/(x+2)=-(3x+8)/(x^2+2x)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275119 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><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=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (2x-5)/(x)+(4x-1)/(x+2)=-(3x+8)/(x^(2)+2x)\r<BR>\n" );
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document.write( "Factor out the GCF of x from each term in the polynomial.<BR>\n" );
document.write( "(2x-5)/(x)+(4x-1)/(x+2)=-(3x+8)/(x(x)+x(2))\r<BR>\n" );
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document.write( "Factor out the GCF of x from x^(2)+2x.<BR>\n" );
document.write( "(2x-5)/(x)+(4x-1)/(x+2)=-(3x+8)/(x(x+2))\r<BR>\n" );
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document.write( "Find the LCD (least common denominator) of ((2x-5))/(x)+((4x-1))/((x+2))-((3x+8))/(x(x+2)).<BR>\n" );
document.write( "Least common denominator: x(x+2)\r<BR>\n" );
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document.write( "Multiply each term in the equation by x(x+2) in order to remove all the denominators from the equation.<BR>\n" );
document.write( "(2x-5)/(x)*x(x+2)+(4x-1)/(x+2)*x(x+2)=-(3x+8)/(x(x+2))*x(x+2)\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "6x^(2)-2x-10=-(3x+8)/(x(x+2))*x(x+2)\r<BR>\n" );
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document.write( "Simplify the right-hand side of the equation by simplifying each term.<BR>\n" );
document.write( "6x^(2)-2x-10=-3x-8\r<BR>\n" );
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document.write( "Since -3x contains the variable to solve for, move it to the left-hand side of the equation by adding 3x to both sides.<BR>\n" );
document.write( "6x^(2)-2x-10+3x=-8\r<BR>\n" );
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document.write( "Since -2x and 3x are like terms, subtract 3x from -2x to get x.<BR>\n" );
document.write( "6x^(2)+x-10=-8\r<BR>\n" );
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document.write( "To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.<BR>\n" );
document.write( "6x^(2)+x-2=0\r<BR>\n" );
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document.write( "In this problem (2)/(3)*-(1)/(2)=-2 and (2)/(3)-(1)/(2)=1, so insert (2)/(3) as the right hand term of one factor and -(1)/(2) as the right-hand term of the other factor.<BR>\n" );
document.write( "(x+(2)/(3))(x-(1)/(2))=0\r<BR>\n" );
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document.write( "Remove the fraction by multiplying the first term of the factor by the denominator of the second term.<BR>\n" );
document.write( "(3x+2)(2x-1)=0\r<BR>\n" );
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document.write( "Set each of the factors of the left-hand side of the equation equal to 0.<BR>\n" );
document.write( "3x+2=0_2x-1=0\r<BR>\n" );
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document.write( "Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.<BR>\n" );
document.write( "3x=-2_2x-1=0\r<BR>\n" );
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document.write( "Divide each term in the equation by 3.<BR>\n" );
document.write( "(3x)/(3)=-(2)/(3)_2x-1=0\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "x=-(2)/(3)_2x-1=0\r<BR>\n" );
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document.write( "Set each of the factors of the left-hand side of the equation equal to 0.<BR>\n" );
document.write( "x=-(2)/(3)_2x-1=0\r<BR>\n" );
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document.write( "Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.<BR>\n" );
document.write( "x=-(2)/(3)_2x=1\r<BR>\n" );
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document.write( "Divide each term in the equation by 2.<BR>\n" );
document.write( "x=-(2)/(3)_(2x)/(2)=(1)/(2)\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "x=-(2)/(3)_x=(1)/(2)\r<BR>\n" );
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document.write( "The complete solution is the set of the individual solutions.<BR>\n" );
document.write( "x=-(2)/(3),(1)/(2) </SPAN>\n" );
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