Decompose 1 / (x + 1)(x² - x + 1) into partial fractions.
Q1. Decompose 1 / (x + 1)(x² - x + 1) into partial fractions.
Answer: 1 / 3(x + 1) + (2 - x) / 3(x² - x + 1)
Explanation: Using partial fractions for a linear and an irreducible quadratic factor, 1 / (x + 1)(x² - x + 1) = A / (x + 1) + (Bx + C) / (x² - x + 1).