Question

When solving (x/9) - (4/3) = x - (5/6) can I multiply by 3 instead of 9 to get rid of the fractions, since all the denominators are multiples of 3?

Answer 1

When you multiply by 3 you don't get rid of the fractions

Step-by-step explanation:

The given expression is

`(x)/(9)-(4)/(3)=x-(5)/(6)`

If we multiply by 3, we get:

`\begin{gathered} 3((x)/(9))-3((4)/(3))=3x-3((5)/(6)) \\ \\ (x)/(3)-4=3x-(5)/(2) \end{gathered}`

Therefore, when we multiply by 3 we don't get rid of all of the denominators. To get rid of all of the denominators, we will need to multiply by 18 which is the minimum common multiple of 9, 3, and 6. Multiplying by 18, we get:

`\begin{gathered} 18((x)/(9))-18((4)/(3))=18x-18((5)/(6)) \\ \\ 2x-24=18x-15 \end{gathered}`