Math & Science ⇒ Problem with displaying brackets in fractions

[Bill21]

Hi!
I need display fraction with multiple levels and brackets in some levels. If i use standart left, right constructions, i have ugly fraction. I have a lot of empty place in brackets. Below you see example and tex code. What do I need to change to correct display this fraction?

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\frac{u}{v}=\frac{y_0}{x_0} + \cfrac{k_0}{\cfrac{x_0}{\left( \cfrac{y_1}{x_1}+\cfrac{k_1}{\cfrac{x_1}{\left(\cfrac{y_2}{x_2}+\cfrac{k_2}{\left(\ddots + \cfrac{k_{n-1}}{\cfrac{x_{n-1}y_n}{x_n}}\right)}\right)}}\right)}}

[Bartman]

A minimal working example marked as code (LaTeX tags are more suitable for inline code) improves the chance to get help.

You can omit the parentheses, use the array environment inside each pair of parentheses, or work with the \scaleleftright command of the scalerel package.