AQA Paper 1 2023 June — Question 7

Exam BoardAQA
ModulePaper 1 (Paper 1)
Year2023
SessionJune
TopicIndices and Surds

7
  1. Given that \(n\) is a positive integer, express $$\frac { 7 } { 3 + 5 \sqrt { n } } - \frac { 7 } { 5 \sqrt { n } - 3 }$$ as a single fraction not involving surds.
    7
  2. Hence, deduce that $$\frac { 7 } { 3 + 5 \sqrt { n } } - \frac { 7 } { 5 \sqrt { n } - 3 }$$ is a rational number for all positive integer values of \(n\)