Manipulating Form of output expressions

Suppose I get the output expression as: $$z(\Delta)=\frac{1+gk^2+h}{\Delta+g+U/h}$$

Now I want to write as: $$z(\Delta/k)=\frac{\frac{1}{k}+gk+\frac{h}{k}}{\frac{\Delta}{k}+\frac{g}{k}+\frac{U}{hk}}$$

Now, this is the exact same expression but can Mathematica transform it like this on command?

• If you define z(delta) as above, then z(delta/k) is not equal to the expression you indicate, where you simply divide the numerator and denominator by k Apr 30, 2021 at 15:47
• Because u can write the ratio as totally another parameter and hence it no longer depends on delta but the ratio. Right. Correct. Ah but lets say I still wanted the latter RHS expression.
– Lost
Apr 30, 2021 at 15:56

A combination of pattern matching and the function Distribute can help.

exp = z[Δ] == (1 + g k^2 + h)/(Δ + g + (U/h));

exp /. {z[Δ] -> z[Δ/k], x__Plus :> Distribute[x/k]}
(* z[Δ] == (1/k + h/k + g k)/(g/k + U/(h k) + Δ/k) *)

TeXForm[exp /.{z[Δ] -> z[Δ/k], x__Plus :> Distribute[x/k]}]


$$z\left(\frac{\Delta }{k}\right)=\frac{g k+\frac{h}{k}+\frac{1}{k}}{\frac{g}{k}+\frac{U}{h k}+\frac{\Delta }{k}}$$

Now if you want to control the order exactly more work will need to be done.

• Helps a lot. I'll accept after waiting for more answers. Also, can we make logarithmic y for a parametric plot? There is no LogParametricPlot function like LogPlot.
– Lost
Apr 30, 2021 at 16:07