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Find A  and B such that 5x+2/x^2-7x-30=A/x-10+B/x+3. Write your answer in the form (A,B)

tertre  Mar 1, 2017
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#1
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i gotchu fam a is 18 b is 21 boy to easy

Guest Mar 1, 2017
#2
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tertre  Mar 1, 2017
#3
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You should bracket the terms that are ambiguous, such as:2/x^2-7x. Is it: 2 / (x^2) - 7? or 2/(x^2 - 7)?....etc., so that there is no question as to what you want.

Guest Mar 1, 2017
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tertre  Mar 1, 2017
#5
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The first part : 5x+2/x^2-7x-30... No brackets

tertre  Mar 1, 2017
#6
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Tertre....I believe this is a partial fraction decomposition.....I think we must have.....

( 5x + 2)  / (x^2 - 7x - 30)   =    A / (x - 10)  + B / ( x + 3)

( 5x + 2)  / (x^2 - 7x - 30)   =    [ A(x + 3) + B(x - 10) ] / [ (x - 10) (x +3) ]

Expanding the denominator on the right will produce the denominator on the left so we can ignore these and solve this

5x + 2  =  A(x +3) + B(x - 10)

5x + 2   = (A + B)x  + [ 3A - 10B]

Equate coefficients   and we have the following system :

A + B  = 5     →  B = 5 - A   (1)

3A - 10B  = 2   (2)

Sub (1) into (2)

3A - 10 (5 - A) = 2

3A - 50 + 10A  = 2

13A  =  52     →  A  = 4

And B  =  5 - A   =  5 - 4   = 1

Check for yourself that

4/ ( x - 10) + 1/ ( x + 3)      produces the rational function   [5x + 2] / [ x^2 - 7x - 30 ]

P.S. -  The use of parentheses/brackets would make it easier to figure out what you're asking.......

CPhill  Mar 1, 2017
#7
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Thanks Cphil!! That's what I'm asking.

tertre  Mar 1, 2017

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