Evaluate
\frac{5\left(x+3y\right)}{8\left(x+5y\right)}
Expand
\frac{5\left(x+3y\right)}{8\left(x+5y\right)}
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\frac{\left(5x^{2}+30xy+45y^{2}\right)\left(x+y\right)}{\left(x^{2}+6xy+5y^{2}\right)\left(8x+24y\right)}
Divide \frac{5x^{2}+30xy+45y^{2}}{x^{2}+6xy+5y^{2}} by \frac{8x+24y}{x+y} by multiplying \frac{5x^{2}+30xy+45y^{2}}{x^{2}+6xy+5y^{2}} by the reciprocal of \frac{8x+24y}{x+y}.
\frac{5\left(x+y\right)\left(x+3y\right)^{2}}{8\left(x+y\right)\left(x+3y\right)\left(x+5y\right)}
Factor the expressions that are not already factored.
\frac{5\left(x+3y\right)}{8\left(x+5y\right)}
Cancel out \left(x+y\right)\left(x+3y\right) in both numerator and denominator.
\frac{5x+15y}{8x+40y}
Expand the expression.
\frac{\left(5x^{2}+30xy+45y^{2}\right)\left(x+y\right)}{\left(x^{2}+6xy+5y^{2}\right)\left(8x+24y\right)}
Divide \frac{5x^{2}+30xy+45y^{2}}{x^{2}+6xy+5y^{2}} by \frac{8x+24y}{x+y} by multiplying \frac{5x^{2}+30xy+45y^{2}}{x^{2}+6xy+5y^{2}} by the reciprocal of \frac{8x+24y}{x+y}.
\frac{5\left(x+y\right)\left(x+3y\right)^{2}}{8\left(x+y\right)\left(x+3y\right)\left(x+5y\right)}
Factor the expressions that are not already factored.
\frac{5\left(x+3y\right)}{8\left(x+5y\right)}
Cancel out \left(x+y\right)\left(x+3y\right) in both numerator and denominator.
\frac{5x+15y}{8x+40y}
Expand the expression.
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