Simplification of an algebra

Question

How can this fraction be simplified? $$ \displaystyle \frac {\frac 1c+ \frac 1d}{c+d}$$ .My friend argues with my answer despite working out the answer,.Any other methods applicable

Answer 1

Hint:

write it as:

$$ \frac{1}{c+d}\left(\frac{1}{c}+\frac{1}{d} \right) $$

Answer 2

In a fraction of fractions, you can simplify numerator with numerator and denominator with denominator: $$\frac{\dfrac1c+\dfrac1d}{c+d}=\dfrac{\dfrac{\color{red}{c+d}}{cd}}{\color{red}{c+d}}\genfrac{}{}{0pt}{0}{\leftarrow \text{ simplify}\atop{\strut }}{{\leftarrow \text{ simplify}}\atop \strut}=\frac1{cd}.$$