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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-1" was replaced by "^(-1)".

Rearrange:

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

                v-((1-t)*(1-t^2)^(-1))=0 

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  1-t² 

Put the exponent aside, try to factor  1-t² 

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 :  t²  is the square of  t¹ 

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

Raise to the exponent which was put aside
Factorization becomes :   (1 + t)^-1   •  (1 - t)^-1  

Multiplying Exponential Expressions :

 1.2    Multiply  (1 - t)  by  (1 - t)^-1  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (1-t)  and the exponents are :
          1 , as  (1-t)  is the same number as  (1-t)¹ 
 and   -1
The product is therefore,  (1-t)^(1+(-1)) = (1-t)⁰ 

Any number raised to the zero power is equal to one

Equation at the end of step  1  :

            1     
  v -  ———————————  = 0 
       1 • (t + 1)

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  1 • (t+1)  as the denominator :

          v     v • 1 • (t + 1)
     v =  —  =  ———————————————
          1       1 • (t + 1)  

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:

 v • (t+1) - (1)      vt + v - 1
 ———————————————  =  ———————————
    1 • (t+1)        1 • (t + 1)

Equation at the end of step  2  :

  vt + v - 1
  ——————————  = 0 
    t + 1   

Step  3  :

When a fraction equals zero :

 3.1    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:

  vt+v-1
  —————— • t+1 = 0 • t+1
  (t+1) 

Now, on the left hand side, the  t+1  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   vt+v-1  = 0

Solving a Single Variable Equation :

 3.2     Solve   vt+v-1  = 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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