Beginning Algebra With Applications, Chapter 7, 7.1, Section 7.1, Problem 62

Simplify $\displaystyle \left( \frac{3}{5}x^2 + \frac{1}{6}x - \frac{5}{8} \right) + \left( \frac{2}{5}x^2 + \frac{5}{6}x - \frac{3}{8} \right)$


$
\begin{equation}
\begin{aligned}

\left( \frac{3}{5}x^2 + \frac{1}{6}x - \frac{5}{8} \right) + \left( \frac{2}{5}x^2 + \frac{5}{6}x - \frac{3}{8} \right) =& \left( \frac{3}{5}x^2 + \frac{2}{5}x^2 \right) + \left( \frac{1}{6}x + \frac{5}{6}x \right) + \left( - \frac{5}{8} - \frac{3}{8} \right)
&& \text{Use the commutative and associative properties of addition to rearrange and group like terms.}
\\
\\
=& \frac{5}{5}x^2 + \frac{6}{6}x - \frac{8}{8}
&& \text{ Combine like terms and write the polynomial in descending order.}
\\
\\
=& x^2 + x - 1
&&

\end{aligned}
\end{equation}
$