Question

(x-1)(x-3)(x-4)/(-1)(-3)(-4)

Answer 1

Step  1  :

5 Simplify — 4

Equation at the end of step  1  :

1 x 5 (((—-1)+—)-4)-— = 0 x x 4

Step  2  :

x Simplify — x

Equation at the end of step  2  :

1 5 (((— - 1) + 1) - 4) - — = 0 x 4

Step  3  :

1 Simplify — x

Equation at the end of step  3  :

1 5 (((— - 1) + 1) - 4) - — = 0 x 4

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction 

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

1 1 • x 1 = — = ————— 1 x

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 
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:

1 - (x) 1 - x ——————— = ————— x x

Equation at the end of step  4  :

(1 - x) 5 ((——————— + 1) - 4) - — = 0 x 4

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction 

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

1 1 • x 1 = — = ————— 1 x

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions 

(1-x) + x 1 ————————— = — x x

Equation at the end of step  5  :

1 5 (— - 4) - — = 0 x 4

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction 

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

4 4 • x 4 = — = ————— 1 x

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions 

1 - (4 • x) 1 - 4x ——————————— = —————— x x

Equation at the end of step  6  :

(1 - 4x) 5 ———————— - — = 0 x 4

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple 

      The left denominator is :       x 

      The right denominator is :       4 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 2022 Product of all 
 Prime Factors 144

                  Number of times each Algebraic Factor
            appears in the factorization of:    Algebraic    
    Factor     Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right}  x 101


      Least Common Multiple: 
      4x 

Calculating Multipliers :

 7.2    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 = 4

   Right_M = L.C.M / R_Deno = x

Making Equivalent Fractions :

 7.3      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. (1-4x) • 4 —————————————————— = —————————— L.C.M 4x R. Mult. • R. Num. 5 • x —————————————————— = ————— L.C.M 4x

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions 

(1-4x) • 4 - (5 • x) 4 - 21x ———————————————————— = ——————— 4x 4x

Equation at the end of step  7  :

4 - 21x ——————— = 0 4x

Step  8  :

When a fraction equals zero :

 8.1    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:

4-21x ————— • 4x = 0 • 4x 4x

Now, on the left hand side, the  4x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   4-21x  = 0

Solving a Single Variable Equation :

 8.2      Solve  :    -21x+4 = 0 

 Subtract  4  from both sides of the equation : 
                      -21x = -4 
Multiply both sides of the equation by (-1) :  21x = 4 


Divide both sides of the equation by 21:
                     x = 4/21 = 0.190 

One solution was found :

                   x = 4/21 = 0.190