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There are numbers A and B for which

A/(x - 1) + B/(x + 1) = (2x + 1)/(x^2 - 1)

for every number $x \neq \pm 1$. Find B.

 May 16, 2021
 #1
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A/(x - 1) + B/(x + 1) = (A(x+1) + B(x-1))/(x+1)/(x-1) = (2x + 1)/(x^2 - 1)

A(x+1) + B(x-1) = (2x + 1)

(A+B)x + A - B = 2x + 1

 

A + B = 2

A - B = 1

 

Can you solve B from here?

 

=^._.^=

 May 16, 2021

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