Question

x+3divided by 7 minus x-3 divided by 6=1

Answer 1

x+3divided by 7 minus x-3divided by 6 =1

(x + 3)     (x - 3)
---------  -  ---------   = 1
    7             6

To eliminate the denominators, multiply everyting by 42

42 * (x + 3)    42 *  (x - 3)
----------------  -  ----------------   = 42 * 1
        7                  6

6 * (x + 3)  -  (7  * (x - 3))  =  42

6x + 18  - 7x + 21  = 42
-x + 39  = 42
-x  = 42 - 39  = 3
x = -3

Plug the value of x into the original equation.

(-3 + 3)      (-3 - 3)
-----------  -  ----------   = 1
     7             6

      0            -6
-----------  -  ----------   = 1
     7             6

Although you can't divide by zero, you CAN divide zero
by any number. What you get is zero.

         -6
0  -  ----------   = 1
          6

You are left with

-  (-6 / 6)   = 1
1 = 1

So, x is -3.