#### Answer

$(3x^{2}+x+1)-(2x^{2}-3x-5)=x^{2}+4x+6$

#### Work Step by Step

$(3x^{2}+x+1)-(2x^{2}-3x-5)$
Change the sign of the terms in the second parentheses and simplify by combining like terms:
$(3x^{2}+x+1)-(2x^{2}-3x-5)=3x^{2}+x+1-2x^{2}+3x+5$
$...=x^{2}+4x+6$