$\frac{ 2 \times \frac{ 1 }{ x }+3{y}^{-1} }{ 9{x}^{2}-4{y}^{2} }$
Any expression raised to the power of $-1$ equals its reciprocal$\frac{ 2 \times \frac{ 1 }{ x }+3 \times \frac{ 1 }{ y } }{ 9{x}^{2}-4{y}^{2} }$
Calculate the product$\frac{ \frac{ 2 }{ x }+3 \times \frac{ 1 }{ y } }{ 9{x}^{2}-4{y}^{2} }$
Calculate the product$\frac{ \frac{ 2 }{ x }+\frac{ 3 }{ y } }{ 9{x}^{2}-4{y}^{2} }$
Write all numerators above the least common denominator $xy$$\frac{ \frac{ 2y+3x }{ xy } }{ 9{x}^{2}-4{y}^{2} }$
Simplify the complex fraction$\frac{ 2y+3x }{ xy \times \left( 9{x}^{2}-4{y}^{2} \right) }$
Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression$\frac{ 2y+3x }{ xy \times \left( 3x-2y \right) \times \left( 3x+2y \right) }$
Cancel out the common factor $3x+2y$$\frac{ 1 }{ xy \times \left( 3x-2y \right) }$
Distribute $xy$ through the parentheses$\frac{ 1 }{ 3{x}^{2}y-2x{y}^{2} }$