Question:
What is the common denominator of
in the complex fraction
![$(y+(y-3)/(3))/((5)/(y)+(2)/(3 y))$](https://img.qammunity.org/2021/formulas/mathematics/middle-school/cabrhvbfzfctoaeizlrslbirulmie40mq8.png)
A)
![$3 y(y-3)$](https://img.qammunity.org/2021/formulas/mathematics/middle-school/3sq8icwmcqgt8q2vqozyejaaanmnoj92j0.png)
B)
![$y(y-3)$](https://img.qammunity.org/2021/formulas/mathematics/middle-school/khwynvigvs5ovpcj203wcdwwldobpgs0d4.png)
C)
![3y](https://img.qammunity.org/2021/formulas/mathematics/middle-school/4r2rk6vp0nvnhe276y5br4icoitlg9z522.png)
D)
![3](https://img.qammunity.org/2021/formulas/mathematics/middle-school/iqv29hrfsc6ps2xd84gabd3efiep5uq89f.png)
Answer:
Option D : 3 is the common denominator
Step-by-step explanation:
It is given that the complex fraction
![$(y+(y-3)/(3))/((5)/(y)+(2)/(3 y))$](https://img.qammunity.org/2021/formulas/mathematics/middle-school/cabrhvbfzfctoaeizlrslbirulmie40mq8.png)
We need to determine the common denominator of
from the complex fraction.
Let us consider the fraction
![$y+(y-3)/(3)$](https://img.qammunity.org/2021/formulas/mathematics/middle-school/f26fv74o7dshsr131a4by452tzi682jahe.png)
To find the common denominator, let us take LCM.
Thus, rewriting the above fraction as,
![(y)/(1) +(y-3)/(3)$](https://img.qammunity.org/2021/formulas/mathematics/middle-school/slsmxg73g5ufwh2sqd16he7u6xe0m1hyu4.png)
The LCM can be determined by multiplying the denominators.
Thus, we get,
![1*3=3](https://img.qammunity.org/2021/formulas/mathematics/middle-school/w15sp7mhuoocr2yinm0lk2jz11q9wo1vdp.png)
Thus, the common denominator is 3.
Hence, Option D is the correct answer.