Express (2x-1)/(x-1)(2x-3) in partial fractions.

The general form of the partial fractions we want is A/(x-1) + B/(2x-3), where A and B are constants we need to find the values of.

We know that A/(x-1) + B/(2x-3) = (2x-1)/(x-1)(2x-3), so we can conclude that A(2x-3) + B(x-1) = 2x - 1

The best way to solve for A and B now is to equate the coefficients on each side of the equation. On the left, we have 2A + B x's, while we have 2x on the right. This means that 2A + B = 2.

Similarly, we have that -3A - B = -1.

We now have a pair of simultaneous equations to solve in A and B. If we add together the above equations, we get -A = 1, which implies that A = -1. We can then obtain that B = 2. Putting these values into the general equation for the partial fractions gives -1/(x-1) + 2/(2x-3), which is our answer.

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