Let $0 \le a \le 1$ and $0 \le b \le 1.$  Find the largest possible value of
\[\frac{a + b}{ab + 1}.\]
Question:
Let $0 \le a \le 1$ and $0 \le b \le 1.$  Find the largest possible value of
\[\frac{a + b}{ab + 1}.\]
Answer:
Let's think step by step.

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Let $0 \le a \le 1$ and $0 \le b \le 1.$  Find the largest possible value of
\[\frac{a + b}{ab + 1}.\]
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