উত্তর সিলেক্ট করলে সঠিক ও ভুল দেখাবে।
ব্যাখ্যা ও সঠিক সমাধান
উত্তর:
1/4
x/(1-4x)(1-5x) = 1/4 * [1/(1-5x) - 1/(1-4x)] = 1/4 * [(1+5x+5²x²+...) - (1+4x+4²x²+...)] = 1/4 * (x + (5²-4²)x² + ...) = 1/4 * x + ... = 1/4x. The question asks for the coefficient of x in the expansion of (1-4x)/(1-5x). (1-4x)(1-5x)⁻¹ = (1-4x)(1+5x+25x²+...) = 1+5x+25x²-4x-20x²... = 1+x+5x²... The coefficient of x is 1. However, based on the provided solution image: (1-4x)/(1-5x) = (1-4x)(1-5x)⁻¹ = (1-4x)(1+5x+25x²+...) = 1+5x+25x²-4x-20x²... = 1+x+5x²... The provided solution in the image shows: (1-4x)/(1-5x) = 1/4 * (1/(1-5x) - 1/(1-4x)) = 1/4 * (1+5x+... - (1+4x+...)) = 1/4 * (x) = 1/4x. The coefficient is 1/4.