Simplify: 2/3=12/x Tiger Algebra Solver

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 2/3-(12/x)=0

Step by step solution :

Step 1 :

12 Simplify —— x

Equation at the end of step 1 :

2 12 — - —— = 0 3 x

Step 2 :

2 Simplify — 3

Equation at the end of step 2 :

2 12 — - —— = 0 3 x

Step 3 :

Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple The left denominator is : 3 The right denominator is : x

Number of times each prime factor appears in the factorization of:

Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
3	1	0	1
Product of all Prime Factors	3	1	3

Number of times each Algebraic Factor appears in the factorization of:

Algebraic Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
x	0	1	1

Least Common Multiple: 3x

Calculating Multipliers :

3.2 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 = x Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractionsTwo 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. 2 • x —————————————————— = ————— L.C.M 3x R. Mult. • R. Num. 12 • 3 —————————————————— = —————— L.C.M 3x

Adding fractions that have a common denominator :

3.4 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

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

Step 4 :

Pulling out like terms :

4.1 Pull out like factors : 2x - 36 = 2 • (x - 18)

Equation at 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 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:

2•(x-18) ———————— • 3x = 0 • 3x 3x

Now, on the left hand side, the 3x cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape : 2 • (x-18) = 0

Equations which are never true :

5.2 Solve : 2 = 0This equation has no solution. A a non-zero constant never equals zero.

Solving a Single Variable Equation :

5.3 Solve : x-18 = 0Add 18 to both sides of the equation : x = 18

One solution was found :

x = 18