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\frac{5\left(2x+3\right)\times 15y}{3y^{2}\times 4}
Divide \frac{5\left(2x+3\right)}{3y^{2}} by \frac{4}{15y} by multiplying \frac{5\left(2x+3\right)}{3y^{2}} by the reciprocal of \frac{4}{15y}.
\frac{5\times 5\left(2x+3\right)}{4y}
Cancel out 3y in both numerator and denominator.
\frac{25\left(2x+3\right)}{4y}
Multiply 5 and 5 to get 25.
\frac{50x+75}{4y}
Use the distributive property to multiply 25 by 2x+3.
\frac{5\left(2x+3\right)\times 15y}{3y^{2}\times 4}
Divide \frac{5\left(2x+3\right)}{3y^{2}} by \frac{4}{15y} by multiplying \frac{5\left(2x+3\right)}{3y^{2}} by the reciprocal of \frac{4}{15y}.
\frac{5\times 5\left(2x+3\right)}{4y}
Cancel out 3y in both numerator and denominator.
\frac{25\left(2x+3\right)}{4y}
Multiply 5 and 5 to get 25.
\frac{50x+75}{4y}
Use the distributive property to multiply 25 by 2x+3.