Solve for A and B in the partial fraction decomposition: (2x+1)/(x(x−1)) = A/x + B/(x−1)

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) Step 1: Combine the terms on the right side of the equation. 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)) Step 2: Compare the numerator

Solve for A and B in the partial fraction decomposition: (2x+1)/(x(x−1)) = A/x + B/(x−1)

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) Step 1: Combine the terms on the right side of the equation. 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)) Step 2: Compare the numerator

Solved: Solve for A and B in the partial fraction…

Here's a step-by-step solution for each question:

Question 1:
We are given the equation:

\frac{2x+1}{x(x-1)} = \frac{A}{x} + \frac{B}{x-1}

Solve for A and B in the partial fraction decomposition: (2x+1)/(x(x−1)) = A/x + B/(x-1)

Step-by-step solution

Combine the terms on the right side of the equation.

Compare the numerator

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