Decompose the rational expression (2x+1)/(x(x-1)) into partial fractions.

April 8, 2026Mathematics

$Decompose the rational expression (2x+1)/(x(x-1)) into partial fractions.$

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April 8, 2026

Answer

\frac{A}{x} + \frac{B}{x-1} $$

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Question 1: We are given the equation: $\frac{2x+1}{x(x-1)} = \frac{A}{x} + \frac{B}{x-1}$ To find the values of A and B, we combine the terms on the right side: $\frac{A}{x} + \frac{B}{x-1} = \frac{A(x-1) + Bx}{x(x-1)} = \frac{Ax - A + Bx}{x(x-1)} = \frac{(A+B)x - A}{x(x-1)}$ Now, we compare the numerator of

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Here's a step-by-step solution for each question: Question 1: We are given the equation: (2x+1)/(x(x-1)) = (A)/(x) + (B)/(x-1) To find the values of A and B, we combine the terms on the right side: (A)/(x) + (B)/(x-1) = (A(x-1) + Bx)/(x(x-1)) = (Ax -…

Asked on April 8, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 8, 2026

Here's a step-by-step solution for each question: Question 1: We are given the equation: (2x+1)/(x(x-1)) = (A)/(x) + (B)/(x-1) To find the values of A and B, we combine the terms on the right side: (A)/(x) + (B)/(x-1) = (A(x-1) + Bx)/(x(x-1)) = (Ax - A + Bx)/(x(x-1)) = ((A+B)x - A)/(x(x-1)) Now, we compare the numerator of