Contributor Illustrative Mathematics
The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of a car). The given form of the combined fuel economy computation is useful for direct calculation, but is not particularly helpful if you need an approximation. With the reduced form q(x)+r(x)/b(x), it is easy to read off the approximate value as q(x) when r(x)/b(x) is small.
The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of a car). The given form of the combined fuel economy computation is useful for direct calculation, but is not particularly helpful if you need an approximation. With the reduced form q(x)+r(x)/b(x), it is easy to read off the approximate value as q(x) when r(x)/b(x) is small.
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