Evaluate
\frac{27y^{2}+166y+432}{15y\left(y+4\right)}
Expand
\frac{27y^{2}+166y+432}{15y\left(y+4\right)}
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\frac{36+9y}{5y}-\frac{10}{3\left(y+4\right)}
Factor 12+3y.
\frac{\left(36+9y\right)\times 3\left(y+4\right)}{15y\left(y+4\right)}-\frac{10\times 5y}{15y\left(y+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5y and 3\left(y+4\right) is 15y\left(y+4\right). Multiply \frac{36+9y}{5y} times \frac{3\left(y+4\right)}{3\left(y+4\right)}. Multiply \frac{10}{3\left(y+4\right)} times \frac{5y}{5y}.
\frac{\left(36+9y\right)\times 3\left(y+4\right)-10\times 5y}{15y\left(y+4\right)}
Since \frac{\left(36+9y\right)\times 3\left(y+4\right)}{15y\left(y+4\right)} and \frac{10\times 5y}{15y\left(y+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{108y+432+27y^{2}+108y-50y}{15y\left(y+4\right)}
Do the multiplications in \left(36+9y\right)\times 3\left(y+4\right)-10\times 5y.
\frac{166y+432+27y^{2}}{15y\left(y+4\right)}
Combine like terms in 108y+432+27y^{2}+108y-50y.
\frac{166y+432+27y^{2}}{15y^{2}+60y}
Expand 15y\left(y+4\right).
\frac{36+9y}{5y}-\frac{10}{3\left(y+4\right)}
Factor 12+3y.
\frac{\left(36+9y\right)\times 3\left(y+4\right)}{15y\left(y+4\right)}-\frac{10\times 5y}{15y\left(y+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5y and 3\left(y+4\right) is 15y\left(y+4\right). Multiply \frac{36+9y}{5y} times \frac{3\left(y+4\right)}{3\left(y+4\right)}. Multiply \frac{10}{3\left(y+4\right)} times \frac{5y}{5y}.
\frac{\left(36+9y\right)\times 3\left(y+4\right)-10\times 5y}{15y\left(y+4\right)}
Since \frac{\left(36+9y\right)\times 3\left(y+4\right)}{15y\left(y+4\right)} and \frac{10\times 5y}{15y\left(y+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{108y+432+27y^{2}+108y-50y}{15y\left(y+4\right)}
Do the multiplications in \left(36+9y\right)\times 3\left(y+4\right)-10\times 5y.
\frac{166y+432+27y^{2}}{15y\left(y+4\right)}
Combine like terms in 108y+432+27y^{2}+108y-50y.
\frac{166y+432+27y^{2}}{15y^{2}+60y}
Expand 15y\left(y+4\right).
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