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MathNet 2021 — Part 08 Question 66

Math Olympiad Vault · MathNet 2021 — Part 08

Question 66

Consider the expression
$$
\frac{\sqrt{x+1}+\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}}.
$$

Part a. Rationalize the denominator and simplify the expression.

Part b. Evaluate the expression at $x=5/4$.