Clearing of Fractions - Solution / Question

[Guest]

In the following equation, the fractions are cleared by multiplying each term:

x/2 + x/3 + x/6 = 2

Multiplying each term by 2 x 3 x 6, the result is:

3 x 6x + 2 + 6x + 2 x 3x = 2 x 3 x 6 x 2

18x + 12x + 6x = 72

Dividing each term by 6:

3x + 2x + x = 12

6x = 12

x = 2

My question: Is there some steps missing ?

Also, in the problem, another solution is to multiply by the lcm (least common multiple) 6 and immediately get:

3x + 2x + x = 12.

[Guest]

No, there are no steps missing but you really should have seen that 2x3= 6 so that the LCM is 6, not 36. Multiplying by 36 and then dividing by 6 is, of course, exactly the same as multiplying by 6! You get the same answer but using the LCM is much simpler.