Question #03d75

Question

985 views around the world

You can reuse this answer
Creative Commons License

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:

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

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

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