I assume you are asking f(x) = (x^2 + 3x + 5) / (x+2)
Let's assume g(x) = x^2 + 3x + 5 = (x+2)^2 + (1-x)
Therefore, f(x) = g(x) / (x+2) = (x+2) + (1-x) / (x+2)
Let x+2 = t
Then f(t) = t + (3-t) / t = t + 3/t - 1, where t ≠ 0
Therefore, the graph is shown in the first attachment.
Since t = x + 2
Your final graph will be 2 units shifted to the left of f(t), which is the second graph:
