If $$ {a={1+x over 2-x}}$$, then find the value $$ {1 over {a+1}}+{2a+1 over{a^{2}-1}}$$ ?

• A. $$ {(1+x)(2+x) over {2x-1}}$$
• B. $$ {(1-x)(2-x) over {x-1}}$$
• C. $$ {(1+x)(2-x) over {2x-1}}$$
• D. $$ {(1+x)(2-x) over {2x+1}}$$