Compute the sum 1/(x+2) + 3/(x-2) and express as a single fraction.

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Study for the 8th Grade Mathematics Test. Prepare with multiple choice questions, each with hints and explanations. Get ready for your exam!

Multiple Choice

Compute the sum 1/(x+2) + 3/(x-2) and express as a single fraction.

Explanation:
Combining fractions requires a common denominator. For 1/(x+2) and 3/(x-2), the common denominator is (x+2)(x-2) = x^2 - 4. Rewrite each fraction with that denominator: 1/(x+2) becomes (x-2)/(x^2-4), and 3/(x-2) becomes 3(x+2)/(x^2-4). Add the numerators: (x-2) + 3(x+2) = x-2 + 3x + 6 = 4x + 4. The sum is (4x+4)/(x^2-4) = 4(x+1)/(x^2-4). Note x cannot be 2 or -2.

Combining fractions requires a common denominator. For 1/(x+2) and 3/(x-2), the common denominator is (x+2)(x-2) = x^2 - 4. Rewrite each fraction with that denominator: 1/(x+2) becomes (x-2)/(x^2-4), and 3/(x-2) becomes 3(x+2)/(x^2-4). Add the numerators: (x-2) + 3(x+2) = x-2 + 3x + 6 = 4x + 4. The sum is (4x+4)/(x^2-4) = 4(x+1)/(x^2-4). Note x cannot be 2 or -2.

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