SOLUTION: Five divided by the sum of a number and 1, minus the quotient of 3 and the difference of the number and 1 isequal to six times the reciprocal of the difference of the number square

Five divided by the sum of a number and 1, minus the quotient of 3 and the
difference of the number and 1 isequal to six times the reciprocal of the
difference of the number squared and 1. 

Replace "five" by "5", and "six" by "6"

5 divided by the sum of a number and 1, minus the quotient of 3 and the
difference of the number and 1 is equal to 6 times the reciprocal of the
difference of the number squared and 1.

Replace the words "a number" and "the number" by "x"

5 divided by the sum of x and 1, minus the quotient of 3 and the
difference of x and 1 is equal to 6 times the reciprocal of the
difference of x squared and 1.

Replace "the sum of x and 1" by "x+1"

5 divided by x+1, minus the quotient of 3 and the
difference of x and 1 is equal to 6 times the reciprocal of the
difference of x squared and 1.

Replace "the difference of x and 1" by "x-1"

5 divided by x+1, minus the quotient of 3 and x-1 is equal to
6 times the reciprocal of the difference of x squared and 1.

Replace "the difference of x squared and 1" by "x²-1"

5 divided by x+1, minus the quotient of 3 and x-1 is equal to
6 times the reciprocal of x²-1.

Replace "5 divided by x+1" by "5/(x+1)

5/(x+1) minus the quotient of 3 and x-1 is equal to
6 times the reciprocal of x²-1.

Replace "the quotient of 3 and x-1" by "3/(x-1)"

5/(x+1) minus 3/(x-1) is equal to
6 times the reciprocal of x²-1

Replace "the reciprocal of x²-1 by 1/(x²-1)

5/(x+1) minus 3/(x-1) is equal to
6 times 1/(x²-1)

Replace "6 times 1/(x²-1)" by "6/(x²-1)

5/(x+1) minus 3/(x-1) is equal to
6/(x²-1)

Replace the word minus by "-", and "is equal to" by "="

5/(x+1) - 3/(x-1) = 6/(x²-1)

Can you solve that?

         5     3     6
        ——— - ——— = ————
        x+1   x-1   x²-1

Factor the denominator on the right:

         5     3        6
        ——— - ——— = ——————————
        x+1   x-1   (x-1)(x+1)

Multiply through by the LCD of (x-1)(x+1)

  5(x-1) - 3(x+1) = 6

  5x - 5 - 3x - 3 = 6

           2x - 8 = 6

               2x = 14

                x = 7

Edwin
AnlytcPhil@aol.com