Which is a correct simplification of 1/α + 1/β?

Which is a correct simplification of 1/α + 1/β?

• A. (α+β)/αβ
• B. α/β + β/α
• C. αβ/(α+β)
• D. α/α + β/β

Answer: (A)

When adding fractions with different denominators, use a common denominator. For 1/α + 1/β, take αβ as the common denominator. Rewriting each fraction: 1/α = β/αβ and 1/β = α/αβ. Adding them gives (β + α)/αβ, which is (α + β)/(αβ). This is the simplified form. The other expressions don’t match this sum: α/β + β/α is a different quantity; αβ/(α+β) is the reciprocal of the sum; α/α + β/β equals 1 + 1 = 2 (assuming α and β are nonzero).

When adding fractions with different denominators, use a common denominator. For 1/α + 1/β, take αβ as the common denominator. Rewriting each fraction: 1/α = β/αβ and 1/β = α/αβ. Adding them gives (β + α)/αβ, which is (α + β)/(αβ). This is the simplified form. The other expressions don’t match this sum: α/β + β/α is a different quantity; αβ/(α+β) is the reciprocal of the sum; α/α + β/β equals 1 + 1 = 2 (assuming α and β are nonzero).