### 2/3=12/x

This encounters adding, subtracting and also finding the least common multiple.

You are watching: 2/3*12

## Step by step Solution ### Rearrange:

Rearrange the equation by individually what is to the appropriate of the equal authorize from both sides of the equation : 2/3-(12/x)=0

## Step 1 :

12 simplify —— x Equation at the finish of action 1 : 2 12 — - —— = 0 3 x

## Step 2 :

2 simplify — 3Equation in ~ the end of step 2 : 2 12 — - —— = 0 3 x

## Step 3 :

Calculating the Least usual Multiple :3.1 find the Least usual Multiple The left denominator is : 3 The right denominator is : x

Number the times every prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
3101
Product of allPrime Factors313

Number the times each Algebraic Factorappears in the factorization of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
x011

Least usual Multiple: 3x

Calculating multiplier :

3.2 calculation multipliers for the two fractions denote the Least usual Multiple by L.C.M signify the Left Multiplier through Left_M denote the right Multiplier by Right_M signify the Left Deniminator by L_Deno signify the best Multiplier by R_DenoLeft_M=L.C.M/L_Deno=xRight_M=L.C.M/R_Deno=3

Making tantamount Fractions :

3.3 Rewrite the 2 fractions into indistinguishable fractionsTwo fountain are referred to as equivalent if they have actually the very same numeric value. For example : 1/2 and 2/4 room equivalent, y/(y+1)2 and also (y2+y)/(y+1)3 are identical as well. To calculate equivalent portion , main point the numerator of each fraction, through its particular Multiplier.

L. Mult. • L. Num. 2 • x —————————————————— = ————— L.C.M 3x R. Mult. • R. Num.

12 • 3 —————————————————— = —————— L.C.M 3x including fractions that have actually a common denominator :3.4 adding up the two equivalent fractions include the two indistinguishable fractions i beg your pardon now have actually a usual denominatorCombine the molecule together, put the sum or difference over the typical denominator then minimize to lowest state if possible:

2 • x - (12 • 3) 2x - 36 ———————————————— = ——————— 3x 3x

## Step 4 :

Pulling out prefer terms :4.1 pull out choose factors:2x - 36=2•(x - 18)

Equation in ~ the end of step 4 : 2 • (x - 18) ———————————— = 0 3x

## Step 5 :

When a fraction equals zero :5.1 when a fraction equals zero ...Where a portion equals zero, that is numerator, the component which is above the fraction line, must equal zero.Now,to eliminate the denominator, Tiger multiplys both political parties of the equation through the denominator.Here"s how:

2•(x-18) ———————— • 3x = 0 • 3x 3x Now, top top the left hand side, the 3x cancels the end the denominator, while, ~ above the appropriate hand side, zero times anything is still zero.The equation now takes the shape:2 • (x-18)=0

Equations which are never ever true:5.2Solve:2=0This equation has actually no solution. A a non-zero constant never equates to zero.

Solving a solitary Variable Equation:5.3Solve:x-18 = 0Add 18 to both sides of the equation:x = 18