(a^1/2 + a^−1/2) / (1 − a)  +  (1 − a^−1/2) / (1 + √a)  is equal to :(a^1/2 + a^−1/2) / (1 − a)  +  (1 − a^−1/2) / (1 + √a)  बराबर है :

1. Aa / (a − 1)
2. B(a − 1) / 2
3. C2 / (a − 1)
4. D2 / (1 − a)

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Show answer & explanation

Correct answer: D. 2 / (1 − a)

Explanation

Put x = √a, so a = x². The first term becomes (x + 1/x) ÷ (1 − x²) and the second (1 − 1/x) ÷ (1 + x). Taking the common denominator x(1 − x)(1 + x), the numerator is (x² + 1) + (x − 1)(1 − x) = x² + 1 − 1 + 2x − x² = 2x, so the sum is 2x ÷ [x(1 − x²)] = 2 / (1 − a).मान लीजिए x = √a, अर्थात् a = x²। पहला पद (x + 1/x) ÷ (1 − x²) तथा दूसरा (1 − 1/x) ÷ (1 + x) बन जाता है। सामान्य हर x(1 − x)(1 + x) लेने पर अंश = (x² + 1) + (x − 1)(1 − x) = x² + 1 − 1 + 2x − x² = 2x, अतः योग = 2x ÷ [x(1 − x²)] = 2 / (1 − a)।