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

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

Question 1:
We are given the equation:

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

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