Question

`(3x - 2)/((x + 3)(x - 1)(x + 2))`
resolve this into partial fraction
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Answer 1

`(-11)/(4(x+3))+(1)/(12(x-1))+(8)/(3(x+2))`

Explanation:

`(3x - 2)/((x + 3)(x - 1)(x + 2))=(A)/(x+3)+(B)/(x-1)+(C)/(x+2)\\\\A=(3(-3)-2)/((-3-1)(-3+2))=(-11)/(4)\\\\B=(3(1)-2)/((1+3)(1+2))=(1)/(12)\\\\C=(3(-2)-2)/((-2+3)(-2-1))=(-8)/(-3)=(8)/(3)\\\\(3x - 2)/((x + 3)(x - 1)(x + 2))=\boxed{(-11)/(4(x+3))+(1)/(12(x-1))+(8)/(3(x+2))}`

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When the denominator factors are linear and to the first degree, the corresponding coefficient can be found by eliminating that factor and evaluating the expression for the value of x that would make the factor zero.

As we showed above, the coefficient A is found by evaluating the expression for x=-3 (the zero of the denominator of A) with that factor eliminated from the denominator. Likewise for the others.