Find the partial fraction decomposition of x-3/x(x^2+3)

Answer:-1 / x + (x + 1) / (x² + 3)Step-by-step explanation:(x − 3) / (x (x² + 3))There are two factors in the denominator, so split this into two fractions with unknown numerators:A / x + (Bx + C) / (x² + 3)Combine back into one fraction:(A (x² + 3) + (Bx + C) x) / (x (x² + 3))Now equate this numerator with the original:A (x² + 3) + (Bx + C) x = x − 3Ax² + 3A + Bx² + Cx = x − 3(A + B) x² + Cx + 3A = x − 3Match the coefficients:A + B = 0C = 13A = -3Solve:A = -1B = 1C = 1Therefore, the partial fraction decomposition is:-1 / x + (x + 1) / (x² + 3)Here's a graph showing that the two are the same:desmos.com/calculator/hrxfnijewh