Which is the expression for 1/α + 1/β + 1/γ?

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Boost your skills in A Level Further Mathematics Core Pure. Study with flashcards and multiple choice questions, each question is followed by hints and explanations. Get prepared for your exam with confidence!

Multiple Choice

Which is the expression for 1/α + 1/β + 1/γ?

Explanation:
Add the three fractions using a common denominator. The common denominator is αβγ, so rewrite each term as 1/α = βγ/(αβγ), 1/β = αγ/(αβγ), and 1/γ = αβ/(αβγ). Putting them together gives (βγ + αγ + αβ) / (αβγ), which is the same as (αβ + βγ + αγ) / αβγ. This matches the expression given. The other forms would misrepresent the numerator or invert the overall fraction, so this is the correct sum.

Add the three fractions using a common denominator. The common denominator is αβγ, so rewrite each term as

1/α = βγ/(αβγ), 1/β = αγ/(αβγ), and 1/γ = αβ/(αβγ).

Putting them together gives

(βγ + αγ + αβ) / (αβγ),

which is the same as (αβ + βγ + αγ) / αβγ. This matches the expression given. The other forms would misrepresent the numerator or invert the overall fraction, so this is the correct sum.

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