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Is it true or false that `(x^2+1)/(x+1) = x`

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spock14 | Student, Undergraduate | (Level 1) eNoter

Posted May 3, 2012 at 6:21 PM via web

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Is it true or false that `(x^2+1)/(x+1) = x`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 3, 2012 at 6:27 PM (Answer #1)

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It is not true that `(x^2+1)/(x+1) = x` for all values of x.

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

=> `x^2 + 1 = x^2 + x`

=> `x = 1`

Only for x = 1, `(x^2+1)/(x+1) = x` . This is not the case for a general value of x.

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classsic | Student, Undergraduate | (Level 3) eNoter

Posted May 3, 2012 at 10:46 PM (Answer #2)

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no (x^2+1)/(x+1)

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

the (x+1) in the denominator and numerator cancel out, so you are left with x-1 which is the answer.

 

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