decompose expression into a sum of partial fraction -22/`(x^(2)+3x-28)`  

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`x^2+3x-28`

`= x^2+7x-4x-28`

`= x(x+7)-4(x+7)`

`= (x+7)(x-4)`

 

`(-22)/(x^2+3x-28) = (-22)/((x+7)(x-4))`

`(-22)/(x^2+3x-28) = A/(x+7)+B/(x-4)`

`-22 = A(x-4)+B(x+7)`


When x = 4

`-22 = Bxx11`

`B = -2`

 

When x = -7

`-22 = Axx(-11)`

`A = 2`

 

So the answer is;

`(-22)/(x^2+3x-28) = 2/(x+7)-2/(x-4)`

 

 

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