If (√$(a+x)$ + √$(a-x)$)/(√$(a+x)$ − √$(a-x)$) = 2, then $x$ : a equals:

By componendo and dividendo the ratio becomes (2√$(a+x)$)/(2√$(a-x))=(2+1)/(2-1)=3$. Squaring, $(a+x)/(a-x)=9$, so $a+x=9a-9x$, giving $10x=8a$ and $x:a=4$ : 5. (Stopping at the un-squared value 3 gives 3 : 1, and 9 : 1 is the squared ratio, not $x$ : a.) Check with $a=5,x=4:(3+1)/(3-1)=2$.