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Write 3x - 8/(x^2 - 3x) in the partial fraction form.

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peterf299 | Student, Grade 11 | (Level 1) Salutatorian

Posted September 12, 2013 at 4:11 PM via web

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Write 3x - 8/(x^2 - 3x) in the partial fraction form.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 12, 2013 at 4:17 PM (Answer #1)

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The expression `(3x - 8)/(x^2 - 3x)` has to be written in the partial fraction form.

Factoring x^2 - 3x gives x*(x - 3)

Let `(3x - 8)/(x^2 - 3x) = A/x + B/(x - 3)`

=> `(3x - 8)/(x^2 - 3x) = (A*(x - 3) + B*x)/(x*(x - 3))`

=> 3x - 8 = Ax - 3A + Bx

`A + B = 3` and `-3A = -8 => A = 8/3`

B = `3 - 8/3 = 1/3`

The partial fraction form of `(3x - 8)/(x^2 - 3x) = 8/(3*x) + 1/(3*(x - 3))`

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