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There are numbers A and B for which

A/(x - 1) + B/(x + 1) = (8x + 3)/(x^2 - 1)

for every number $x^2 \neq 1$. Find B.

 Jul 26, 2021
 #1
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A/(x - 1) + B/(x + 1) = (8x + 3)/(x^2 - 1)      Multiply both sides of the equation by (x^2-1)

 

A (x+1)   + B (x-1)  = 8x+3

Ax + A    +  Bx -B = 8x+3                equat the 'x' parts   and the constant parts

 

A+B = 8       and     A-B = 3     <======= two equations two unknowns.....solve for A and B

 

Add the two equations   2A = 11      so     A = 5.5   then B = 2.5

 Jul 26, 2021

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