# If [(x-1)/(x+1)] + [(x+1)/(x-1)] is written as mixed number A B/C, then B=______

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should write `(x-1)/(x+1) + (x+1)/(x-1)`  as a mixed number that consists in a combination of a whole number and a proper fraction, such that:

`(x-1)/(x+1) + (x+1)/(x-1) = ((x-1)(x-1) + (x+1)(x+1))/((x-1)(x+1))`

`(x-1)/(x+1) + (x+1)/(x-1)= ((x-1)^2 + (x+1)^1)/(x^2-1)`

Expanding the binomials to numerator yields:

`(x-1)/(x+1) + (x+1)/(x-1) = (x^2-2x+1+x^2+2x+1)/(x^2-1)`

`(x-1)/(x+1) + (x+1)/(x-1) = (2x^2+2)/(x^2-1)`

Factoring out 2 yields:

`(x-1)/(x+1) + (x+1)/(x-1) = 2(x^2+1)/(x^2-1)`

Hence, since the result is a mixed number, you may identify the whole number as `A = 2` , the numerator of the fraction `B = x^2+1`   and the denominator `C = x^2-1` .

Hence, converting the given expression in a mixed number yields that `B = x^2+1.`

thi-dallas | Student, Undergraduate | (Level 1) Valedictorian

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For fraction:

a/b + b/a = 2 + [(b-a)^2]/ab

b=x+1

a=x-1

Then b-a = x+1 -x+1=2 and 2^2 = 4

the answer = 2 + 4/[(x+1)(x-1)] = A B/C

=> B =4