Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :Â
                     3/x-1-5*x/x+2-(1/4)=0Â
Step by step solution :Step  1  : 1
Simplify —
4
Equation at the end of step  1  : 3 x 1
(((—-1)-(5•—))+2)-— = 0
x x 4
Step  2  : x
Simplify —
x
Equation at the end of step  2  : 3 1
(((—-1)-(5•1))+2)-— = 0
x 4
Step  3  : 3
Simplify —
x
Equation at the end of step  3  : 3 1
(((— - 1) - 5) + 2) - — = 0
x 4
Step  4  :Rewriting the whole as an Equivalent Fraction :
 4.1   Subtracting a whole from a fractionÂ
Rewrite the whole as a fraction using  x  as the denominator :
1 1 • x
1 = — = —————
1 x
Equivalent fraction :Â The fraction thus generated looks different but has the same value as the wholeÂ
Common denominator :Â 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 fractionsÂ
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:
3 - (x) 3 - x
——————— = —————
x x
Equation at the end of step  4  : (3 - x) 1
((——————— - 5) + 2) - — = 0
x 4
Step  5  :Rewriting the whole as an Equivalent Fraction :
 5.1   Subtracting a whole from a fractionÂ
Rewrite the whole as a fraction using  x  as the denominator :
5 5 • x
5 = — = —————
1 x
Adding fractions that have a common denominator :
 5.2      Adding up the two equivalent fractionsÂ
(3-x) - (5 • x) 3 - 6x
——————————————— = ——————
x x
Equation at the end of step  5  : (3 - 6x) 1
(———————— + 2) - — = 0
x 4
Step  6  :Rewriting the whole as an Equivalent Fraction :
 6.1   Adding a whole to a fractionÂ
Rewrite the whole as a fraction using  x  as the denominator :
2 2 • x
2 = — = —————
1 x
Step  7  :Pulling out like terms :
 7.1    Pull out like factors :
   3 - 6x  =   -3 • (2x - 1)Â
Adding fractions that have a common denominator :
 7.2      Adding up the two equivalent fractionsÂ
-3 • (2x-1) + 2 • x 3 - 4x
——————————————————— = ——————
x x
Equation at the end of step  7  : (3 - 4x) 1
———————— - — = 0
x 4
Step  8  :Calculating the Least Common Multiple :
 8.1   Find the Least Common MultipleÂ
     The left denominator is :       xÂ
     The right denominator is :       4Â
        Number of times each prime factor
        appears in the factorization of: PrimeÂ
 Factor  LeftÂ
 Denominator  RightÂ
 Denominator  L.C.M = MaxÂ
 {Left,Right} 2022 Product of allÂ
 Prime Factors 144                  Number of times each Algebraic Factor
            appears in the factorization of:    Algebraic   Â
    Factor     LeftÂ
 Denominator  RightÂ
 Denominator  L.C.M = MaxÂ
 {Left,Right}  x 101
     Least Common Multiple:Â
      4xÂ
Calculating Multipliers :
 8.2   Calculate multipliers for the two fractionsÂ
   Denote the Least Common Multiple by  L.C.MÂ
   Denote the Left Multiplier by  Left_MÂ
   Denote the Right Multiplier by  Right_MÂ
   Denote the Left Deniminator by  L_DenoÂ
   Denote the Right Multiplier by  R_DenoÂ
   Left_M = L.C.M / L_Deno = 4
   Right_M = L.C.M / R_Deno = x
Making Equivalent Fractions :
 8.3     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.Â
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (3-4x) • 4
—————————————————— = ——————————
L.C.M 4x
R. Mult. • R. Num. x
—————————————————— = ——
L.C.M 4x
Adding fractions that have a common denominator :
 8.4      Adding up the two equivalent fractionsÂ
(3-4x) • 4 - (x) 12 - 17x
———————————————— = ————————
4x 4x
Equation at the end of step  8  : 12 - 17x
———————— = 0
4x
Step  9  :When a fraction equals zero : 9.1   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:
12-17x
—————— • 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 :
   12-17x  = 0
Solving a Single Variable Equation :
 9.2      Solve  :    -17x+12 = 0Â
 Subtract  12 from both sides of the equation :Â
                      -17x = -12Â
Multiply both sides of the equation by (-1) :Â Â 17x = 12Â
Divide both sides of the equation by 17:
                     x = 12/17 = 0.706Â
One solution was found :Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â x = 12/17 = 0.706