How do you write $(3x)/((x + 2)(x - 1))$ as a partial fraction decomposition?

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Answer 1 · 2016-08-04T13:28:42

$= 2/(x+2) + 1/(x-1)$

$(3x)/((x+2)(x-1)) = A/(x+2) + B/(x-1)$

Getting every term over common denominator yields:

$3x = A(x-1) + B(x+2)$

When I do these I eliminate one bracket by setting x to a particular value, but there are many other methods.

$color(red)(x = 1: )$

$3 = 3B implies B = 1$

$color(red)(x=-2: )$

$-6 = -3A implies A = 2$

So $(3x)/((x+2)(x-1)) = 2/(x+2) + 1/(x-1)$

How do you write (3x)/((x + 2)(x - 1))(3x)/((x + 2)(x - 1)) as a partial fraction decomposition?