Question

What is the common denominator of y+((y-3)/3) in the complex fraction (y+((y-3)/3))/((5/9)+(2/3y))=? a) 3y(y-3) b) y(y-3) c) 3y d) 3

Answer 1

The common denominator of
`\(y + (y-3)/(3)\)` in the complex fraction
`\((y + (y-3)/(3))/((5)/(9) + (2)/(3y))\) is \(3y(y-3)\)`, so the correct option is (a) (3y(y-3).

Step-by-step explanation:

To find the common denominator in the complex fraction, we need to identify the factors that would make both denominators the same. In this case, the denominators are 3 and 3y. The common denominator that incorporates both is 3y, as it includes the factor of 3 and also the factor of y.

To arrive at this common denominator, we multiply the first fraction
`\((y-3)/(3)\) by \((y)/(y)\)` (which is equivalent to multiplying by 1 to make the denominator 3 the same as the second denominator 3y. This results in the expression
`\((y^2 - 3y)/(3y)\)`. Now, the common denominator for the complex fraction is 3y.

In conclusion, the common denominator (3y(y-3) is obtained by combining the factors from both original denominators, ensuring that both fractions have the same denominator in the complex fraction. Therefore, option (a) (3y(y-3) is the correct choice.