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There are numbersA and B for which
Ax1+Bx+1=x+2x21
for every number x\neq\pm1.
Find B.

 

Ax1+Bx+1=x+2x21|x21=(x1)(x+1)Ax1+Bx+1=x+2(x1)(x+1)|(x1)(x+1)A(x+1)+B(x1)=x+21. x=1:02B=1+22B=1B=122. x=1:2A+0=1+22A=3A=32

 

laugh

 May 13, 2021
edited by heureka  May 13, 2021

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