Question 330704
a + {{{1/(a+1/a)}}}
:
We want the denominator to be a single fraction over a common denominator
a + {{{1/((a^2+1)/a)}}}
:
Invert the dividing fraction and multiply
a + 1 * {{{a/(a^2+1)}}}
which is:
a + {{{(1a)/(a^2+1)}}} = a + {{{a/(a^2+1)}}}
:
A single fraction over a common denominator:
{{{(a(a^2+1) + a)/(a^2+1)}}} = {{{(a^3 + a + a)/(a^2+1)}}} = {{{(a^3 + 2a)/(a^2+1)}}}
Factor out a in the numerator
{{{(a(a^2 + 2))/(a^2+1)}}}