(3x^2+7) / ((x-1)(x^2+2x+5))

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- May 28th 2008, 03:58 PMcityisminedecompose fraction question
(3x^2+7) / ((x-1)(x^2+2x+5))

- May 28th 2008, 05:41 PMJonboy
what's stumpin' ya?

- May 28th 2008, 08:33 PMcityismine
I can decompose fractions of the type A/(x-1)+ B/(x^2+2x+5) but I'm having trouble with fractions of the type A/(x-1)+(Bx+c)(x^2+2x+5). Can someone show me a step by step method of decomposing fractions of the (Bx+C) type?

- May 28th 2008, 09:59 PMcityismine
Finally figured it out. Answer is 5/(4(x-1)) + (7x-3)/(4(x^2+2x+5)). Hope I'm right.

- May 28th 2008, 10:40 PMChris L T521
I'm going to verify your answer:

Multiply both sides by the denominator of the left term:

Now, we get:

We now compare the coefficients:

From the first equation, we see that . From the third equation, we see that . Now substitute these values for B and C into the second equation:

Thus, and

Thus the PFD is:

.

It's Good!! :D