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\frac{1}{2x+3y}
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\frac{1}{2x+3y}
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\frac{2}{2x+3y}-\frac{4x^{2}-6xy+9y^{2}}{\left(2x+3y\right)\left(4x^{2}-6xy+9y^{2}\right)}
Factor the expressions that are not already factored in \frac{4x^{2}-6xy+9y^{2}}{8x^{3}+27y^{3}}.
\frac{2}{2x+3y}-\frac{1}{2x+3y}
Cancel out 4x^{2}-6xy+9y^{2} in both numerator and denominator.
\frac{1}{2x+3y}
Since \frac{2}{2x+3y} and \frac{1}{2x+3y} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 2 to get 1.
\frac{2}{2x+3y}-\frac{4x^{2}-6xy+9y^{2}}{\left(2x+3y\right)\left(4x^{2}-6xy+9y^{2}\right)}
Factor the expressions that are not already factored in \frac{4x^{2}-6xy+9y^{2}}{8x^{3}+27y^{3}}.
\frac{2}{2x+3y}-\frac{1}{2x+3y}
Cancel out 4x^{2}-6xy+9y^{2} in both numerator and denominator.
\frac{1}{2x+3y}
Since \frac{2}{2x+3y} and \frac{1}{2x+3y} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 2 to get 1.
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