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There are numbers A and B for which A/(x - 1) + B/(x + 1) = (x + 3)/(x^2 - 1) for every number x other than 1 and -1. Find .A - B.

 Aug 3, 2022

Best Answer 

 #1
avatar+2446 
+1

We have the equation \({A \over (x - 1)} + {B \over (x + 1)} = {(x + 3) \over (x^2 - 1)}\)

 

Multiply by \(x^2 -1\)\(A(x+1) + B(x-1) = x + 3\)

 

From this, we know that \(A + B = 1\) and \(A - B = 3\), so \(A - B = \color{brown}\boxed{3}\)

 Aug 3, 2022
 #1
avatar+2446 
+1
Best Answer

We have the equation \({A \over (x - 1)} + {B \over (x + 1)} = {(x + 3) \over (x^2 - 1)}\)

 

Multiply by \(x^2 -1\)\(A(x+1) + B(x-1) = x + 3\)

 

From this, we know that \(A + B = 1\) and \(A - B = 3\), so \(A - B = \color{brown}\boxed{3}\)

BuilderBoi Aug 3, 2022

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