Simplify \(\frac{1}{2}(2{x}^{2}+x-2)\) to \(\frac{2{x}^{2}+x-2}{2}\).
\[\frac{2{x}^{2}+x-2}{2}+\frac{1}{3}(4{x}^{2}-3x-2)\]
Simplify \(\frac{1}{3}(4{x}^{2}-3x-2)\) to \(\frac{4{x}^{2}-3x-2}{3}\).
\[\frac{2{x}^{2}+x-2}{2}+\frac{4{x}^{2}-3x-2}{3}\]
Simplify using the common denominator.
\[\frac{3(2{x}^{2}+x-2)+2(4{x}^{2}-3x-2)}{6}\]
Expand.
\[\frac{6{x}^{2}+3x-6+8{x}^{2}-6x-4}{6}\]
Collect like terms.
\[\frac{(6{x}^{2}+8{x}^{2})+(3x-6x)+(-6-4)}{6}\]
Simplify \((6{x}^{2}+8{x}^{2})+(3x-6x)+(-6-4)\) to \(14{x}^{2}-3x-10\).
\[\frac{14{x}^{2}-3x-10}{6}\]
(14*x^2-3*x-10)/6
