\[\left| x^{2} - 2x + 3 \right| + \left| - x^{2} - 5 \right| =\]
\[= \left| x^{2} - 2x + 3 \right| + \left| x^{2} + 5 \right| =\]
\[= x^{2} - 2x + 3 + x^{2} + 5 =\]
\[= 2x^{2} - 2x + 8.\]
\[Дополнительные\ вычисления:\]
\[x^{2} - 2x + 3 =\]
\[= \left( x^{2} - 2x + 1 \right) + 2 =\]
\[= (x - 1)^{2} + 2 > 0\]
\[x^{2} + 5 > 0\ для\ любого\ x.\]