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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     x^2/121+y^2/71-(1)=0 

Step  1  :

            y2
 Simplify   ——
            71

Equation at the end of step  1  :

   (x2)    y2     
  (———— +  ——) -  1  = 0 
   121     71     
 Step  2  :
             x2
 Simplify   ———
            121

Equation at the end of step  2  :

    x2    y2     
  (——— +  ——) -  1  = 0 
   121    71     

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       121 

      The right denominator is :       71 

      Least Common Multiple:
      8591 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 71

   Right_M = L.C.M / R_Deno = 121

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      x2 • 71
   ——————————————————  =   ———————
         L.C.M              8591  

   R. Mult. • R. Num.      y2 • 121
   ——————————————————  =   ————————
         L.C.M               8591  

Adding fractions that have a common denominator :

 3.4       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:

 x2 • 71 + y2 • 121     71x2 + 121y2
 ——————————————————  =  ————————————
        8591                8591    

Equation at the end of step  3  :

  (71x2 + 121y2)    
  —————————————— -  1  = 0 
       8591         

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  8591  as the denominator :

         1     1 • 8591
    1 =  —  =  ————————
         1       8591  

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 :

 4.2       Adding up the two equivalent fractions

 (71x2+121y2) - (8591)     71x2 + 121y2 - 8591
 —————————————————————  =  ———————————————————
         8591                     8591        

Trying to factor a multi variable polynomial :

 4.3    Factoring    71x² + 121y² - 8591 

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

 Factorization fails

Equation at the end of step  4  :

  71x2 + 121y2 - 8591
  ———————————————————  = 0 
         8591        

Step  5  :

When a fraction equals zero :

 5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  71x2+121y2-8591
  ——————————————— • 8591 = 0 • 8591
       8591      

Now, on the left hand side, the  8591  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   71x²+121y²-8591  = 0

Solving a Single Variable Equation :

 5.2     Solve   71x²+121y²-8591  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

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