SSC CGL Tier I 12 Sep 2025 Shift 3 Paper

Concept:Rationalize the sum of two fractions with binomial denominators using the conjugate property: (a + b)(a - b) = a² - b².Explanation:First, combine the fractions over a common denominator. Write: $$\frac{1}{5+\sqrt{3}} + \frac{1}{5-\sqrt{3}} = \frac{(5-\sqrt{3}) + (5+\sqrt{3})}{(5+\sqrt{3})(5-\sqrt{3})}$$. Simplify the numerator: $5 - \sqrt{3} + 5 + \sqrt{3} = 10$. Simplify the denominator: $(5)^2 - (\sqrt{3})^2 = 25 - 3 = 22$. So the expression becomes $\frac{10}{22}$. Reduce the fraction by dividing numerator and denominator by 2: $\frac{5}{11}$.Answer:Option A: $5/11$