Word Count : 505

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हम दिए गए भिन्न को आंशिक भिन्नों (Partial Fractions) के रूप में व्यक्त करेंगे: \[ \frac{x-1}{x^3 - x^2 - 2x} \] ### चरण 1: हर (Denominator) को कारक करना हर को सरल करने के लिए, हम इसका फैक्टराइजेशन करेंगे: \[ x^3 - x^2 - 2x = x (x^2 - x - 2) \] अब, \( x^2 - x - 2 \) को फैक्टर करें: \[ x^2 - x - 2 = (x - 2)(x + 1) \] तो, हमारा हर (denominator) हो गया: \[ x (x - 2)(x + 1) \] ### चरण 2: आंशिक भिन्नों के रूप में अभिव्यक्ति करना हम मान लेते हैं कि भिन्न को निम्नलिखित रूप में लिखा जा सकता है: \[ \frac{x-1}{x (x - 2)(x + 1)} = \frac{A}{x} + \frac{B}{x ______ _____ __________ ______ ____ ____ ____.
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