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Find the partial fraction decomposition of the rational function. 2/(x-1)(x+1)

User Jyriand
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Final answer:

To decompose the function 2/(x-1)(x+1), we find constants A and B such that the function equals A/(x-1) + B/(x+1). By solving for A and B, we find that the partial fraction decomposition is 1/(x-1) - 1/(x+1).

Step-by-step explanation:

To find the partial fraction decomposition of the rational function 2/(x-1)(x+1), we assume that it can be represented as the sum of two simpler fractions:

A/(x-1) + B/(x+1)

Now we need to determine the constants A and B. We do this by multiplying both sides by the common denominator (x-1)(x+1) to get:

2 = A(x+1) + B(x-1)

Next, we solve for A and B by choosing suitable values for x. For instance, if we put x=1, we get:

2 = A(2), which means A = 1.

If we put x=-1, we get:

2 = -B(2), which means B = -1.

Hence, the partial fraction decomposition is:

1/(x-1) - 1/(x+1)

User Havrl
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