Problem

Analyze \((3x~+~7)/(x~+~2)~=~3~+~1/(x~+~2)\). State the trend, remainder, correction, restriction, correction limit, asymptote, and multiplication identity.

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Trend: y=1/(x+2). Remainder: 3. Correction: 3. Restriction: x≠-2. Claimed correction limit: 0. Claimed asymptote: y=1/(x+2). Claimed identity: (x+2)·1+3=3x+7.

Trend: y=3. Remainder: 1. Correction: 1/(x+2). Restriction: x≠-2. Claimed correction limit: 1. Claimed asymptote: y=1. Identity: 3(x+2)+1=3x+7.

Trend: y=3. Remainder: 1. Correction: 1/(x+2). Restriction: none; x=-2 is included. Correction limit: 0. Asymptote: y=3. Identity: 3(x+2)+1=3x+7.

Trend: y=3. Remainder: 1. Correction: 1/(x+2). Restriction: x≠-2. Correction limit: 0. Asymptote: y=3. Identity: 3(x+2)+1=3x+7.

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Analyze \((3x~+~7)/(x~+~2)~=~3~+~1/(x~+~2)\). State the trend, remainder, correction, restriction, correction limit, asymptote, and multiplication identity.

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