Question

solve for x
x/6=(x+3)/9

Please help

Answer 1

this equals to 6

Answer 2

how?

Answer 3

ready?

Answer 4

yeah

Answer 5

One solution was found :
x = 6

Rearrange :

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

x/6-((x+3)/9)=0
Step by step solution :
Step 1 :

x x+3
Simplify — - ———
6 9

Calculating the Least Common Multiplier :

1.1 Find the Least Common Multiple (L.C.M)

The left denominator is : 6

The right denominator is : 9

Factor the left and right denominators, counting
the number of times each factor appears :

|———————————————|—————————————————————————————————————|
| | Number of times each prime factor |
| | appears the factorization of: |
| | |
| Prime | Left Right L.C.M = Max |
| Factors |Denominator Denominator {Left,Right}|
| —————————— |——————————— ——————————— ————————————|
| 2 | 1 0 1 |
| 3 | 1 2 2 |
|———————————————|—————————————————————————————————————|
|Product of all | |
| Prime Factors | 6 9 18 |
|———————————————|—————————————————————————————————————|

Least Common Multiple: 18

Calculating Multipliers :

1.2 Calculate multipliers for the two fractions

L.C.M
L. Multiplier = —————————————— = 3
L. Denominator


L.C.M
R. Multiplier = —————————————— = 2
R. Denominator

Making Equivalent Fractions :

1.3 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. x • 3
—————————————————— = —————
L.C.M 18

R. Mult. • R. Num. (x+3) • 2
—————————————————— = —————————
L.C.M 18

Adding fractions that have a common denominator :

1.4 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:

x • 3 - ((x+3) • 2) x - 6
——————————————————— = —————
18 18

Equation at the end of step 1 :

x - 6
————— = 0
18

Step 2 :

x-6
Solve ——— = 0
18

When a fraction equals zero :

2.1 When a fraction equals zero ...

Where a fraction equals zero, its nominator, 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:

x-6
——— • 18 = 0 • 18
18

Now, on the left hand side, the 18 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
x-6 = 0
Solving a Single Variable Equation :

2.2 Solve : x-6 = 0

Add 6 to both sides of the equation :
x = 6