The common denominator of the given expression is [tex]5y+6.[/tex]
Given expression,
[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }[/tex].
We have to find the common denominator.
On solving the numerator and denominator of the given expression,
[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{\frac{3y+y-3}{3} }{\frac{5y+6}{9y} }[/tex]
[tex]= \dfrac{\frac{4y-3}{3} }{\frac{5y+6}{9y} }[/tex]
[tex]= \dfrac{4y-3}{3} \times\dfrac{9y}{5y+6}[/tex]
Or,[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{3y(4y-3)}{5y+6}[/tex]
Hence the common denominator of the above expression is given by [tex]5y+6.[/tex]
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https://brainly.com/question/357568
