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There are numbersA and B for whichAx−1+Bx+1=x+2x2−1for every number x\neq\pm1.Find B.
Ax−1+Bx+1=x+2x2−1|x2−1=(x−1)(x+1)Ax−1+Bx+1=x+2(x−1)(x+1)|∗(x−1)(x+1)A(x+1)+B(x−1)=x+21. x=−1:0−2B=−1+2−2B=1B=−122. x=1:2A+0=1+22A=3A=32