Question

Add:$\frac{5}{16c}+\frac{3}{8c{d}^2}$

Short answer

The Addition of rational expressions is$\frac{5{\mathrm{d}}^2+6}{16c{d}^2}$.

Step-by-step solution

Given information 

The given rational expressions

=$\frac{5}{16c}+\frac{3}{8c{d}^2}$.

Addition of rational expression is 

$$\begin{gathered} 16c=2\times 2\times 2\times 2\times c \\ 8c{d}^2=2\times 2\times 2\times c\times d\times d \\ \mathrm{The}\mathrm{LCD}\mathrm{is}16c{d}^2 \\ \mathrm{Rewrite}\mathrm{each}\mathrm{rational}\mathrm{expression}\mathrm{as}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{the}\mathrm{LCD}. \\ =\frac{5\times {\mathrm{d}}^2}{16\mathrm{c}\times {\mathrm{d}}^2}+\frac{3\times 2}{8{\mathrm{cd}}^2\times 2} \\ =\frac{5{\mathrm{d}}^2}{16{\mathrm{cd}}^2}+\frac{6}{16{\mathrm{cd}}^2} \\ =\frac{5{\mathrm{d}}^2+6}{16{\mathrm{cd}}^2} \end{gathered}$$