### Instruction: Express as a common fraction:         $\cfrac{ \frac{2}{5}+\frac{3}{4} }{ \frac{4}{9}+\frac{1}{6}}$.### Response: To simplify a complex fraction, I can multiply the numerator and denominator by the lowest common denominator of all the fractions involved.
The lowest common denominator of $\frac{2}{5}$, $\frac{3}{4}$, $\frac{4}{9}$, and $\frac{1}{6}$ is 180.
Multiplying the numerator and denominator by 180, I get $\cfrac{ \frac{2}{5}+\frac{3}{4} }{ \frac{4}{9}+\frac{1}{6}} = \cfrac{ 2\cdot 36 + 3 \cdot 45 }{ 4 \cdot 20 + 1 \cdot 30 }$.
Simplifying the arithmetic, I get $\cfrac{ 72 + 135 }{ 80 + 30 } = \cfrac{ 207 }{ 110 }$.