Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.71" was replaced by "(371/100)". 3 more similar replacement(s)

Rearrange:

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

           (149/100)/(179/100)-((371/100)/x)=0 

Step by step solution :

Step  1  :

            371
 Simplify   ———
            100

Equation at the end of step  1  :

  149   179   371
  ——— ÷ ——— - ——— ÷ x  = 0 
  100   100   100

Step  2  :

         371      
 Divide  ———  by  x
         100      

Equation at the end of step  2  :

  149   179    371
  ——— ÷ ——— - ————  = 0 
  100   100   100x

Step  3  :

            179
 Simplify   ———
            100

Equation at the end of step  3  :

  149   179    371
  ——— ÷ ——— - ————  = 0 
  100   100   100x

Step  4  :

            149
 Simplify   ———
            100

Equation at the end of step  4  :

  149   179     371
  ——— ÷ ——— -  ————  = 0 
  100   100    100x

Step  5  :

         149      179
 Divide  ———  by  ———
         100      100

 5.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

149     179       149     100
———  ÷  ———   =   ———  •  ———
100     100       100     179

Equation at the end of step  5  :

  149     371
  ——— -  ————  = 0 
  179    100x

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       179 

      The right denominator is :       100x 

      Least Common Multiple:
      17900x 

Calculating Multipliers :

 6.2    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 = 100x

   Right_M = L.C.M / R_Deno = 179

Making Equivalent Fractions :

 6.3      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.      149 • 100x
   ——————————————————  =   ——————————
         L.C.M               17900x  

   R. Mult. • R. Num.      371 • 179
   ——————————————————  =   —————————
         L.C.M              17900x  

Adding fractions that have a common denominator :

 6.4       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:

 149 • 100x - (371 • 179)     14900x - 66409
 ————————————————————————  =  ——————————————
          17900x                  17900x    

Equation at the end of step  6  :

  14900x - 66409
  ——————————————  = 0 
      17900x    

Step  7  :

When a fraction equals zero :

 7.1    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:

  14900x-66409
  ———————————— • 17900x = 0 • 17900x
     17900x   

Now, on the left hand side, the  17900x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   14900x-66409  = 0

Solving a Single Variable Equation :

 7.2      Solve  :    14900x-66409 = 0 

 Add  66409  to both sides of the equation : 
                      14900x = 66409
Divide both sides of the equation by 14900:
                     x = 66409/14900 = 4.457

One solution was found :