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Step-by-step explanation: Changes made to your input should not affect the SOLUTION:

(1): "X2"   was replaced by   "x^2".  1 more similar replacement(s).

STEP

1

:

            8

Simplify   ——

           x2

Equation at the end of step

1

:

           8      

 ((x6) -  ——) -  2

          x2      

STEP  

2

:

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  x2  as the denominator :

          x6     x6 • x2

    x6 =  ——  =  ———————

          1        x2    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding FRACTIONS that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x6 • x2 - (8)     x8 - 8

—————————————  =  ——————

     x2             x2  

Equation at the end of step

2

:

 (x8 - 8)    

 ———————— -  2

    x2        

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  x2  as the denominator :

        2     2 • x2

   2 =  —  =  ——————

        1       x2  

Trying to factor as a Difference of Squares:

3.2      Factoring:  x8 - 8  

Theory : A difference of two perfect squares,  A2 - B2  can be FACTORED into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 8 is not a square !!