Answer
$$\frac{5}{10n^2+16n+6}+\frac{n-6}{10n^2+16n+6}=\frac{n-1}{10n^2+16n+6}$$
Explanation
| $$ \begin{aligned}\frac{5}{10n^2+16n+6}+\frac{n-6}{10n^2+16n+6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{n-1}{10n^2+16n+6}\end{aligned} $$ | |
| ① | Add $ \dfrac{5}{10n^2+16n+6} $ and $ \dfrac{n-6}{10n^2+16n+6} $ to get $ \dfrac{n-1}{10n^2+16n+6} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{5}{10n^2+16n+6} + \frac{n-6}{10n^2+16n+6} & = \frac{5}{\color{blue}{10n^2+16n+6}} + \frac{n-6}{\color{blue}{10n^2+16n+6}} = \\[1ex] &=\frac{ 5 + \left( n-6 \right) }{ \color{blue}{ 10n^2+16n+6 }}= \frac{n-1}{10n^2+16n+6} \end{aligned} $$ |
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