¿Una mano con polinomios?

Se suman coeficiente a coeficiente:

a)

$$\begin{align}&A(x)+B(x)=3x^2+\frac 56x -x^2+\frac 13x-1=\\ &\\ &\\ &2x^2 + \left ( \frac 56 + \frac 13 \right )x-1=\\ &\\ &\\ &2x^2 + \left ( \frac {15+6}{18} \right )x-1=\\ &\\ &\\ &\\ &2x^2 + \left ( \frac {21}{18} \right )x-1=\\ &\\ &\\ &2x^2 + \frac 76 x-1=\\ &\\ &\\ &\end{align}$$

b)

$$\begin{align}&A(x)-C(x) = 3x^2+ \frac 56 x-\left  ( \frac 23 x^2 -2 \right )=\\ &\\ &\\ &3x^2+ \frac 56 x-\frac 23 x^2 +2=\\ &\\ &\\ &\left( 3- \frac 23 \right)x^2+ \frac 56 x + 2 =\\ &\\ &\\ &\left( \frac{9-2}{3} \right)x^2+ \frac 56 x + 2 =\\ &\\ &\\ &\frac 72 x^2+ \frac 56 x + 2\\ &\\ &\\ &\\ &\end{align}$$

c)

$$\begin{align}&3A(x)-2B(x)+5C(x) =\\ &\\ &3 \left( 3x^2+ \frac 56 x\right)-2 \left (-x^2+ \frac 13x-1 \right )+ 5 \left( \frac 23 x^2-2\right)=\\ &\\ &\\ &9x^2+\frac{15}{6}x+2x^2-\frac 23 x+2+\frac{10}{3}x^2-10=\\ &\\ &\\ &\left( 11+ \frac{10}{3} \right )x^2+ \left(\frac{15}{6}-\frac 23  \right)x-8 =\\ &\\ &\\ &\left( \frac{33+10}{3} \right )x^2+ \left ( \frac{15-4}{6}  \right)x-8 =\\ &\\ &\\ &\frac {43}{3}x^2+ \frac{11}{6}x-8\\ &\\ &\\ &\end{align}$$

Y eso es todo.