Question

Add:$\frac{2}{15a^{2}b}+\frac{5}{6a{b}^2}$

Short answer

The addition of rational expressions is $\frac{4b+25a}{30a^2{b}^2}$.

Step-by-step solution

Given Information

The given expressions is$\frac{2}{15a^{2}b}+\frac{5}{6a{b}^2}$.

Simplify the expression 

$$\begin{gathered} 15a^{2}b\mathrm{can}\mathrm{be}\mathrm{written}\mathrm{as}3\times 5\times \mathrm{a}\times \mathrm{a}\times \mathrm{b} \\ 6{\mathrm{ab}}^2\mathrm{can}\mathrm{be}\mathrm{written}\mathrm{as}2\times 3\times \mathrm{a}\times \mathrm{b}\times \mathrm{b} \end{gathered}$$

The LCD of $15a^{2}b\mathrm{and}6{\mathrm{ab}}^2$is $30a^2{b}^2$.

Rewrite each rational expression as an equivalent fraction with the LCD .

$$\begin{gathered} =\frac{2\times 2\mathrm{b}}{15{\mathrm{a}}^2\mathrm{b}\times 2\mathrm{b}}+\frac{5\times 5\mathrm{a}}{6{\mathrm{ab}}^2\times 5\mathrm{a}} \\ \mathrm{Simplify} \\ =\frac{4\mathrm{b}}{30{\mathrm{a}}^2{\mathrm{b}}^2}+\frac{25\mathrm{a}}{30{\mathrm{a}}^2{\mathrm{b}}^2} \\ \mathrm{Add}\mathrm{the}\mathrm{rational}\mathrm{expressions} \\ =\frac{4\mathrm{b}+25\mathrm{a}}{30{\mathrm{a}}^2{\mathrm{b}}^2} \end{gathered}$$