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glenn101

Member

Registered: 2008-04-02

Posts: 108

Partial fractions (algebra)

Ok I understand up to here but what are the next steps.

Edit- I need to know the actual steps using some method, but I'm unaware of those steps
I think it becomes

5x+1=A(x+2)+B(x-1)
then I'm not sure.

can somebody please provide the steps.

Thanks in advance,
Glenn

Last edited by glenn101 (2008-04-06 21:11:55)

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Dharshi

Member

Registered: 2006-10-31

Posts: 56

Re: Partial fractions (algebra)

Ok I understand up to here but what are the next steps.

Thanks in advance,
Glenn

its' so easy.
Cancel out the denominators and equate the numertors on both the sides. Then you can find the value of x.

Regards,
Dharshi

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Partial fractions (algebra)

Thank you dharshi, however I want to know the steps involved using an appropriate method. Similar to what I posted.

Last edited by glenn101 (2008-04-06 21:13:14)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Partial fractions (algebra)

You're good up to where you are, and from there you need to consider the x-coefficients and the constant terms separately.

5x+1=A(x+2)+B(x-1) becomes:

5x = Ax + Bx (hence 5 = A+B)
and
1 = 2A - B.

You have two simultaneous equations there, which are solved fairly easily.
Once you have A and B, put them back into the original equation and you're done.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Partial fractions (algebra)

To go over it in full, we have:

What we want is for this to be equal to:

Where A and B are integers.  So we take a guess that this is true:

Now we need to try an find A and B.  If we multiply both sides by (x-1)(x+2), we get:

As mathsyperson said, you could solve this as a systems of equations.  I don't like to however.  What we see is that if x = -2, then the right side becomes A(0) + B(-2 -1) and we can solve for B:

And we get that B = 3.  Similarly, if we let x=1, then we can solve for A getting A = 3.  Thus:

Now you may be asking yourself as I did when I took algebra why you need this.   It is almost entirely used for calculus when taking integrals, but you don't need to worry about that just yet.

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glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Partial fractions (algebra)

Thank you Mathsyperson and Ricky!
thank you for the shown workings out Ricky, it really makes the difference, thanks for that:)
thanks for the use of this Ricky, I am looking forward to calculus:)

Last edited by glenn101 (2008-04-07 19:31:54)

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