Mathematics 2019 JAMB Past Questions - Question 9: Evaluate(x+1/x+1)2 – (x-1/x-1)2

Correct Answer

D

Explanation

To evaluate \( (x+\frac{1}{x+1})^2 - (x-\frac{1}{x-1})^2 \), we can start by expanding the expressions.Expanding \( (x+\frac{1}{x+1})^2 \):\[ (x+\frac{1}{x+1})^2 = x^2 + 2x\frac{1}{x+1} + \left(\frac{1}{x+1}\right)^2 \]Expanding \( (x-\frac{1}{x-1})^2 \):\[ (x-\frac{1}{x-1})^2 = x^2 - 2x\frac{1}{x-1} + \left(\frac{1}{x-1}\right)^2 \]Now, we can subtract the second expression from the first:\[ (x^2 + 2x\frac{1}{x+1} + \left(\frac{1}{x+1}\right)^2) - (x^2 - 2x\frac{1}{x-1} + \left(\frac{1}{x-1}\right)^2) \]Simplifying this expression gives us the result.