document.write( "Question 462619: \r\n" );
document.write( "Combine the rational expressions:\r\n" );
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document.write( "x + 2 x - 4 8(x + 1)\r\n" );
document.write( "————— + ————— + ————————\r\n" );
document.write( "x - 7 7 - x x - 7\r\n" );
document.write( "
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document.write( "
Algebra.Com's Answer #317106 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "\r\n" ); document.write( "x + 2 x - 4 8(x + 1)\r\n" ); document.write( "————— + ————— + ————————\r\n" ); document.write( "x - 7 7 - x x - 7\r\n" ); document.write( "\r\n" ); document.write( "We must get all the denominators the same.\r\n" ); document.write( "\r\n" ); document.write( "Two of the denominators are already the same, \r\n" ); document.write( "but the 7 - x is not the same. So let's work \r\n" ); document.write( "on it:\r\n" ); document.write( "\r\n" ); document.write( " 7 - x\r\n" ); document.write( "\r\n" ); document.write( "First write it in descending order:\r\n" ); document.write( "\r\n" ); document.write( " -x + 7\r\n" ); document.write( "\r\n" ); document.write( "which is really\r\n" ); document.write( "\r\n" ); document.write( " -1x + 7\r\n" ); document.write( "\r\n" ); document.write( "Now factor out -1 (which changes the sign of the 7)\r\n" ); document.write( "\r\n" ); document.write( " -1(x - 7)\r\n" ); document.write( "\r\n" ); document.write( "and we can erase the 1\r\n" ); document.write( "\r\n" ); document.write( " -(x - 7) \r\n" ); document.write( "\r\n" ); document.write( "Now our original problem becomes:\r\n" ); document.write( "\r\n" ); document.write( "x + 2 x - 4 8(x + 1)\r\n" ); document.write( "————— + —————— + ————————\r\n" ); document.write( "x - 7 -(x - 7) x - 7\r\n" ); document.write( "\r\n" ); document.write( "Now take the - sign out in front of\r\n" ); document.write( "that fraction making the + into a -\r\n" ); document.write( "\r\n" ); document.write( "x + 2 x - 4 8(x + 1)\r\n" ); document.write( "————— - ————— + ————————\r\n" ); document.write( "x - 7 x - 7 x - 7\r\n" ); document.write( "\r\n" ); document.write( "Now all the denominators are the same.\r\n" ); document.write( "\r\n" ); document.write( "Distribute out the 8(x + 1) as 8x + 8\r\n" ); document.write( "\r\n" ); document.write( "x + 2 x - 4 8x + 8\r\n" ); document.write( "————— - ————— + ————————\r\n" ); document.write( "x - 7 x - 7 x - 7\r\n" ); document.write( "\r\n" ); document.write( "Put parentheses around the numerators:\r\n" ); document.write( "\r\n" ); document.write( "(x + 2) (x - 4) (8x + 8)\r\n" ); document.write( "——————— - ——————— + ————————\r\n" ); document.write( " x - 7 x - 7 x - 7\r\n" ); document.write( "\r\n" ); document.write( "Combine the numerators over the common \r\n" ); document.write( "denominator:\r\n" ); document.write( "\r\n" ); document.write( "(x + 2) - (x - 4) + (8x + 8)\r\n" ); document.write( "————————————————————————————\r\n" ); document.write( " x - 7\r\n" ); document.write( "\r\n" ); document.write( "Remove the parentheses\r\n" ); document.write( "\r\n" ); document.write( " x + 2 - x + 4 + 8x + 8\r\n" ); document.write( "————————————————————————\r\n" ); document.write( " x - 7\r\n" ); document.write( "\r\n" ); document.write( "Combine like terms:\r\n" ); document.write( "\r\n" ); document.write( " 8x + 14\r\n" ); document.write( " —————————\r\n" ); document.write( " x - 7\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |