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Step by Step Solution

Step  1  :

Equation at the end of step  1  :

  ((((m2)-1)•x)+x•(m-1))+3  < 0 

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  m2-1 

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 : 1 is the square of 1
Check :  m2  is the square of  m1 

Factorization is :       (m + 1)  •  (m - 1) 

Equation at the end of step  2  :

  (x•(m+1)•(m-1)+x•(m-1))+3  < 0 

Step  3  :

Trying to factor a multi variable polynomial :

 3.1    Factoring    m2x - mx + 3 

Try to factor this multi-variable trinomial using trial and error 

 
Factorization fails

Equation at the end of step  3  :

  m2x - mx + 3  < 0 

Step  4  :

Hyperbolic inequality is not implemented yet

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