Question #03d75

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Answer 1 · 2017-09-02T18:40:07

#frac(1 + 2 x^(2) sqrt(x^(2) + 1))(2 (x^(2) + 1))#

We have: #frac((x^(2) + 1)^(- 1))(2) + frac(x^(2))(sqrt(1 + x^(2)))#

#= frac(frac(1)(x^(2) + 1))(2) + frac(x^(2))(sqrt(x^(2) + 1))#

#= frac(1)(2 (x^(2) + 1)) + frac(x^(2))(sqrt(x^(2) + 1))#

Let's rationalise the denominator of the second fraction:

#= frac(1)(2 (x^(2) + 1)) + frac(x^(2) sqrt(x^(2) + 1))(x^(2) + 1)#

#= frac(1)(2 (x^(2) + 1)) + frac(2 x^(2) sqrt(x^(2) + 1))(2 (x^(2) + 1))#

#= frac(1 + 2 x^(2) sqrt(x^(2) + 1))(2 (x^(2) + 1))#