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

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Prepare for the A Level Further Mathematics Core Pure Test with detailed explanations and challenging questions. Boost your understanding and confidence to excel in your exam!

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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