Decompose the rational expression (2x+1)/(x(x−1)) into partial fractions of the form A/x + (B)/(x−1) and find the values of A and B.

Here are the solutions to all the problems from the image. 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: Equate the numerators of both

Decompose the rational expression (2x+1)/(x(x−1)) into partial fractions of the form A/x + (B)/(x−1) and find the values of A and B.

Here are the solutions to all the problems from the image. 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: Equate the numerators of both

Solved: Decompose the rational expression (2x+1)/(x(x−1))…

Here are the solutions to all the problems from the image.

Question 1:
We are given the equation:

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

Decompose the rational expression (2x+1)/(x(x-1)) into partial fractions of the form (A)/(x) + (B)/(x-1) and find the values of A and B.

Step-by-step solution

Combine the terms on the right side of the equation.

Equate the numerators of both

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