Question

What is the common denominator of y StartFraction y minus 3 Over 3 EndFraction in the complex fraction y StartFraction y minus 3 Over 3 EndFraction divided by five-ninths StartFraction 2 Over 3 y EndFraction?.

Answer 1

The common denominator of the given expression is $5y+6.$

Given expression,

$\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }$.

We have to find the common denominator.

On solving the numerator and denominator of the  given expression,

$\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{\frac{3y+y-3}{3} }{\frac{5y+6}{9y} }$

       $= \dfrac{\frac{4y-3}{3} }{\frac{5y+6}{9y} }$

$= \dfrac{4y-3}{3} \times\dfrac{9y}{5y+6}$

Or,$\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{3y(4y-3)}{5y+6}$

Hence the common denominator of the above expression is given by $5y+6.$

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