• Let \(f(x) = \frac {x-1}{3 + x}\) with its natural domain.
  
• Let \(G(t) = -2t + 6\) with its natural domain.
  
• Let \(H(k) = -|2-k|+6\) with its natural domain.
  
• Let \(T(w) = w^2 - 3\) with its natural domain.
  

Let \(a\), \(b\), and \(c\) be positive real numbers such that

• \(a > 2\)
• \(b \ne -3\)
• \(c < 2\)

Evaluate the following. (Use DNE for Does not Exist)

\begin{align*} f(a + 1) &= \answer {\frac {a}{a+4}} \\ f(a) + f(1) &= \answer {\frac {a-1}{3+a}} \\ H(2+a) &= \answer {a+6} \\ H(2) + H(a) &= \answer {14-a} \\ 2 T(b) + 1 &= \answer {2 b^2 - 5} \\ T(2a) - T(a) &= \answer {DNE} \end{align*}

\begin{align*} G(b+c) &= \answer {7-2(b+c)+6} \\ G(b) + G(c) &= \answer {7-2(b+c)+6} \\ H(2-a) &= \answer {-a+6} \\ H(2) - H(a) &= \answer {a-2} \end{align*}