The error is present in second step when cancelling numerator and denominator and the solution of the expression [tex](1+1/x)/(1-1/x^{2} )[/tex] is [tex]x/x-1[/tex].
Given Expression [tex](1+1/x)/(1-1/x^{2} )[/tex] and incorrect solution. and we need to identify the error and solve the expression correctly.
The expression is [tex](1+1/x)/(1-1/x^{2} )[/tex]
In the solution given the second step of cancelling 1's in numerator and denominator is wrong.
The solution which is correct is as under:
[tex](1+1/x)/(1-1/x^{2} )[/tex]
firstly take LCM in numerator and denominator
=[tex](x+1)/x/(x^{2} -1)/x^{2}[/tex]
Now we can write the expression properly.
=[tex](x+1)*x^{2} /(x^{2} -1)*x[/tex]
Power of [tex]x^{2}[/tex] to be deducted from x
=[tex](x+1)*x/(x^{2} -1)[/tex]
Now [tex]x^{2} -1[/tex] can be written as (x+1)(x-1)
=[tex](x+1)*x/(x+1)(x-1)[/tex]
(x+1) will be deducted now from numerator and denominator.
=x/(x-1)
Hence the solution of the given expression is x/(x-1).
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