Many functions use forms that have multiple instances of $x$, including polynomials and rational functions. However, finding the domain and range can be simpler when they are written with only one use of $x$. It can also make transformations more clear.
For example, the polynomial function $f(x) = x^2-10x+35$ can be rewritten as $f(x) = \left(x-5\right)^2+10$.
By composition of functions, I mean that:
$$f(x) = x^2-10x+35$$
But it can be rewritten as a composition of functions on $x$, with each composed function only using $x$ once:
$$f(x)=g(h(i(x)))$$ $$g(x)=x+10$$ $$h(x)=x^2$$ $$i(x)=x-5$$
However, I cannot figure out how some rational functions can be rewritten in this form, such as:
Can any function be written with only one use of $x$?