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3.2.1 Algebra and Functions (A-level only)

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Question 8
a.

Given that nnn is a positive integer, express

52+3n−53n−2 \frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2} 2+3n​5​−3n​−25​

as a single fraction not involving surds.

[5]
b.

Hence, deduce that

52+3n−53n−2 \frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2} 2+3n​5​−3n​−25​

is a rational number for all positive integer values of nnn.

[2]

3.2.1 Algebra and Functions (A-level only) Questions

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