\r\n" );
document.write( "Solve 
\r\n" );
document.write( "I used LCD and got (1x/(x^2 +2x))- (2x +4)/(x^2 + 2x) = 3\r\n" );
document.write( "Then multiplied bith sides by x^2 -2x\r\n" );
document.write( "3x^2 - 5x -4\r\n" );
document.write( "\r\n" );
document.write( "You need to multiply on both sides to begin with, not\r\n" );
document.write( "multiply on the left and fail to on the right. You also\r\n" );
document.write( "should not multiply the LCD out as you did. Here is\r\n" );
document.write( "step by step, what you should have:\r\n" );
document.write( "\r\n" );
document.write( " 1 2\r\n" );
document.write( " ------- - --- = 3\r\n" );
document.write( " x + 2 x \r\n" );
document.write( "\r\n" );
document.write( "Put the 3 over 1 so everything will be a fraction:\r\n" );
document.write( "\r\n" );
document.write( " 1 2 3\r\n" );
document.write( " ------- - --- = ---\r\n" );
document.write( " x + 2 x 1\r\n" );
document.write( "\r\n" );
document.write( "Now get the LCD = x(x + 2) but DON'T multiply it out!\r\n" );
document.write( "That was one thing you did wrong above. Again, don't multiply the LCD out!\r\n" );
document.write( "\r\n" );
document.write( "Instead put it over 1 like this, with a multiplication dot \r\n" );
document.write( "symbol · beside it:\r\n" );
document.write( "\r\n" );
document.write( " x(x + 2) \r\n" );
document.write( "---------- · \r\n" );
document.write( " 1 \r\n" );
document.write( "\r\n" );
document.write( "Now place that whole thing before each terms on the left side AND the right side:\r\n" );
document.write( "\r\n" );
document.write( " x(x + 2) 1 x(x + 2) 2 x(x + 2) 3 \r\n" );
document.write( " ---------- · ------- - ---------- · --- = ---------- · ---\r\n" );
document.write( " 1 x + 2 1 x 1 1 \r\n" );
document.write( " \r\n" );
document.write( "Now you're ready to do some canceling. \r\n" );
document.write( "\r\n" );
document.write( "1. Cancel the black x + 2 into the red (x + 2)\r\n" );
document.write( "2. Cancel the black x into the red x\r\n" );
document.write( "\r\n" );
document.write( " 1 1\r\n" );
document.write( " x(x + 2) 1 x(x + 2) 2 x(x + 2) 3 \r\n" );
document.write( " ---------- · ------- - ---------- · --- = ---------- · ---\r\n" );
document.write( " 1 x + 2 1 x 1 1\r\n" );
document.write( " 1 1\r\n" );
document.write( "\r\n" );
document.write( "Now notice that after canceling, you have only 1's in the denominators.\r\n" );
document.write( "So you can erase all the 1's and like magic all the fractions are gone:\r\n" );
document.write( "\r\n" );
document.write( "1. All that's left in the first term is the red x\r\n" );
document.write( "2. All the's left in the second term is - (x+2)2\r\n" );
document.write( "3. All that's left on the right side is x(x+2)3\r\n" );
document.write( "\r\n" );
document.write( " x - (x + 2)2 = x(x + 2)3\r\n" );
document.write( "\r\n" );
document.write( "It's customary to write numbers before parenthese, not after them,\r\n" );
document.write( "so we write that as\r\n" );
document.write( "\r\n" );
document.write( " x - 2(x + 2) = 3x(x + 2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I'll now dispense with the colors and make everything black:\r\n" );
document.write( "\r\n" );
document.write( " x - 2(x + 2) = 3x(x + 2)\r\n" );
document.write( "\r\n" );
document.write( "Now we're finally ready to multiply things out, but not until now!\r\n" );
document.write( "\r\n" );
document.write( " x - 2x - 4 = 3x² + 6x\r\n" );
document.write( "\r\n" );
document.write( "Can you finish solving that? If not post again asking how.\r\n" );
document.write( "I'll assume you can. You get two solutions x = -4/3 and x = -1\r\n" );
document.write( "\r\n" );
document.write( "[Neither of these answers cause any denominators to become zero\r\n" );
document.write( "when substituted in the original equation, so they are both\r\n" );
document.write( "solutions. Had we gotten x = -2 we would have had to discard\r\n" );
document.write( "it because it would have made the denominator x - 2 become 0.\r\n" );
document.write( "Sometimes this is the case when we multiply through by the LCD,\r\n" );
document.write( "so we should always look to make sure we aren't including an \r\n" );
document.write( "extraneous solution. I thought I'd better warn you about\r\n" );
document.write( "extraneous solutions because you do get them sometimes, but\r\n" );
document.write( "not in this example.]\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
