document.write( "Question 72801This question is from textbook
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\n" ); document.write( "My son is having trouble Solving rational equations.
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\n" ); document.write( "\n" ); document.write( "1. 2 / (x + 2) - (1/x) = (-4) / (x(x + 2))\r
\n" ); document.write( "\n" ); document.write( "2. c - (c/3) + (c/5) = 26\r
\n" ); document.write( "\n" ); document.write( "3. (1/8) + ((5x) / (x +2)) = (5/2)\r
\n" ); document.write( "\n" ); document.write( "4. (k /(k + 1)) + (k/(k - 2)) = 2
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\n" ); document.write( "5. (10/(2y +8)) - ((7y + 8)/(y^(2) - 16)) = (-8 / (2y - 8))\r
\n" ); document.write( "\n" ); document.write( "6. (5/(x+2)) = (-1/(x^(2) +7x+10)) + (3/(-x-5))\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "
Algebra.Com's Answer #52264 by rmromero(383)\"\" \"About 
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document.write( "Solving rational equations.
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document.write( "Here are a few questions he needs help with: 
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document.write( "1. 2 / (x + 2) - (1/x) = (-4) / (x(x + 2)) \r
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document.write( "        2        1         -4
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document.write( "    _______  -  ___  = __________  Multiply each term by the LCD x(x+2)
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document.write( "     x + 2       x      x(x + 2)\r
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document.write( "        2                 1                 -4
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document.write( "    _______ (x(x+2)) -   ___ (x(x+2)) = __________  (x(x+2))
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document.write( "     x + 2                x              x(x + 2)\r
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document.write( "                        2x - 1(x + 2) = -4
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document.write( "                           2x - x - 2 = -4
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document.write( "                                    x -2 = -4
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document.write( "                           x - 2 +  2 = -4 + 2\r
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document.write( "                                    x = -2
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document.write( "2. c - (c/3) + (c/5) = 26 \r
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document.write( "         c       c
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document.write( "    c - ___  +  ___ = 26   Multiply each term by the LCD = 15
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document.write( "         3       5\r
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document.write( "              c           c
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document.write( "    c (15) - ___ (15) +  ___ (15) = 26  (15) 
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document.write( "              3           5\r
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document.write( "    15c - 5c + 3c = 390    Combine like terms
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document.write( "              13c = 390    Divide 13 both sides\r
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document.write( "                c = 30\r
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document.write( "3. (1/8) + ((5x) / (x +2)) = (5/2) \r
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document.write( "        1         5x       5
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document.write( "      _____ +  _______ =  ___  Mulitply each term by the LCD = 8(x+2)
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document.write( "        8       x + 2      2\r
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document.write( "     1                  5x                  5
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document.write( "   _____ (8(x+2)) +  _______ (8(x+2)) =  ___  (8(x+2)) 
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document.write( "     8                 x + 2                2\r
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document.write( "    1(x+2) + 5x(8) = 5(4(x+2))       Multiply (Distribution Property)
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document.write( "           x + 2 + 40x = 20x + 40    Combine like terms
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document.write( "              41x + 2 = 20x + 40     
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document.write( "                 21x = 38
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document.write( "                        38
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document.write( "                   x = ____   
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document.write( "                        21
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document.write( "4. (k /(k + 1)) + (k/(k - 2)) = 2\r
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document.write( "     k          k
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document.write( "   _____  +  ______  = 2 . LCD is (k + 1)(k - 2)
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document.write( "   k + 1      k - 2\r
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document.write( "    k                       k
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document.write( "   _____ (k + 1)(k - 2)+  ______ (k + 1)(k - 2) = 2 (k + 1)(k - 2)
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document.write( "   k + 1                  k - 2\r
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document.write( "        k(k - 2) + k (k + 1) = 2 \"%28k%5E2+-+k+-2%29\"  Mulitply\r
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document.write( "        \"k%5E2+-+2k+%2B+k%5E2+%2B+k+=+2k%5E2+-+2k+-+4\"     Combine like terms\r
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document.write( "\n" );
document.write( "            \"2k%5E2+-+k+=+2k%5E2+-+2k+-+4\"\r
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document.write( "                    k = -4\r
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document.write( "5. (10/(2y +8)) - ((7y + 8)/(y^(2) - 16)) = (-8 / (2y - 8)) \r
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document.write( "       10        7y + 8      -8
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document.write( "     ______ -  _________ = ______
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document.write( "     2y + 8     y^2 - 16   2y - 8\r
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document.write( "        10         7y + 8        -8
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document.write( "     ________ -  __________ = ________ LCD = 2 (y-4)(y+4)
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document.write( "     2(y + 4)    (y-4)(y+4)   2(y - 4)\r
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document.write( "   10                      7y + 8                     -8
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document.write( "________ (2(y-4)(y+4))-  __________ (2(y-4)(y+4))= ________ (2 (y-4)(y+4))
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document.write( "2(y + 4)                 (y-4)(y+4)               2(y - 4)\r
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document.write( "           10(y - 4) - 2(7y + 8) = -8 (y + 4)
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document.write( "           10y - 40 - (14y + 16) = -8y - 32
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document.write( "          10y - 40 - 1(14y + 16) = -8y - 32
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document.write( "             10y - 40 + 14y - 16 = -8y - 32  Combine like terms
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document.write( "                         4y - 56 = -8y - 32
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document.write( "                             12y = 24        divide both sides by 12
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document.write( "                               y = 2\r
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document.write( "6. (5/(x+2)) = (-1/(x^(2) +7x+10)) + (3/(-x-5)) \r
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document.write( "     5            -1              3
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document.write( "   _____ = ______________  +  ________
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document.write( "   x + 2    x^2 + 7x + 10      -x - 5\r
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document.write( "    5            -1               3
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document.write( "   _____ = ______________  +  _________   LCD = -1(x + 5)(x + 2)
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document.write( "   x + 2   (x + 5)(x + 2)     -1(x + 5)\r
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document.write( "     5                            -1                                  3
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document.write( "   _____ (-1(x + 5)(x + 2)) = ______________ (-1(x + 5)(x + 2)) +  _________ (-1(x + 5)(x + 2))
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document.write( "   x + 2                      (x + 5)(x + 2)                       -1(x + 5)\r
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document.write( "              5 (-1(x + 5)) = -1 (-1) + 3 (x + 2)\r
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document.write( "             -5x - 25 = 1 + 3x + 6\r
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document.write( "             -5x - 25 = 3x + 7\r
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document.write( "                 -32 = 8x\r
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document.write( "                  -4 = x  \r
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