I have not seen mathematician's method before either but I do like it!!
Which trig function
Do you mean
2+[(3x+y)/(x+y)] ??
=[2(x+y)+(3x+y)](x+y)
=(2x+2y+3x+y)/(x+y)
=(5x+3y)/(x+y)
and that is about it.
Well, you could convert it by hand.
6.3083.... *10^28
You cannot solve it because there is no equal sign.
A lot of school calcs have fractions buttons and you can reduce fractions with it easily.
How this is done depends on the calc.
this post might help you
http://web2.0calc.com/questions/it-just-doesn-t-make-sense-to-me#r2
there is a toggle button down the bottom of the calc to put it into degrees or radians.
Your brackets are unbalanced but this is what I have interpreted.
$$\\\sqrt{\sqrt{3+1}^2+(3-1)^2}\\\\ =\sqrt{\sqrt{4}^2\;\;+\;\;(2)^2}\\\\ =\sqrt{4+4}\\\\ =\sqrt{4*2}\\\\ =2\sqrt{2}\\\\$$
a+a+2b=2a+2b