Let $a,$ $b,$ and $c$ be distinct real numbers.  Simplify the expression
\[\frac{(x + a)^2}{(a - b)(a - c)} + \frac{(x + b)^2}{(b - a)(b - c)} + \frac{(x + c)^2}{(c - a)(c - b)}.\]
<|im_start|>system
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<|im_start|>user
Let $a,$ $b,$ and $c$ be distinct real numbers.  Simplify the expression
\[\frac{(x + a)^2}{(a - b)(a - c)} + \frac{(x + b)^2}{(b - a)(b - c)} + \frac{(x + c)^2}{(c - a)(c - b)}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
Let $a,$ $b,$ and $c$ be distinct real numbers.  Simplify the expression
\[\frac{(x + a)^2}{(a - b)(a - c)} + \frac{(x + b)^2}{(b - a)(b - c)} + \frac{(x + c)^2}{(c - a)(c - b)}.\]
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