Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

Step  2  :

            2my - 2mx - y2 + yx
 Simplify   ———————————————————
                 y2 - 4m2      

Trying to factor as a Difference of Squares :

 2.1      Factoring:  y² - 4m² 

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 : 4 is the square of 2
Check :  y²  is the square of  y¹ 

Check :  m²  is the square of  m¹ 

Factorization is :       (y + 2m)  •  (y - 2m) 

Final result :

  2my - 2mx - y2 + yx
  ———————————————————
  (2m + y) • (y - 2m)