Simiplify. \( \frac{\frac{1}{d}+\frac{1}{e}}{\frac{d^{2}-e^{2}}{d e}} \) The simplified expression is

To simplify the expression \( \frac{\frac{1}{d}+\frac{1}{e}}{\frac{d^{2}-e^{2}}{d e}} \), we first combine the fractions in the numerator: \[ \frac{1}{d} + \frac{1}{e} = \frac{e + d}{de} \] Now, our expression becomes: \[ \frac{\frac{e + d}{de}}{\frac{d^{2}-e^{2}}{de}} \] Since both the numerator and denominator have \( de \), they cancel out, leading to: \[ \frac{e + d}{d^{2} - e^{2}} \] Realizing that \( d^{2} - e^{2} \) can be factored using the difference of squares: \[ d^{2} - e^{2} = (d - e)(d + e) \] Thus, the expression simplifies to: \[ \frac{e + d}{(d - e)(d + e)} \] The final simplified expression is: \[ \frac{1}{d - e} \] if we provided that \( d \neq e \).