How to simplify the equation of a moving vertex if its object is squeezed?

I originally had this equation: startPoint + direction * t;

Where t is a range float that goes from 0 to 1. The idea was to get a point defined by t between a start point and an end point. However, then I discovered that these lines were curves... so the whole thing became more and more complicated:

 void ShowCurveEquation()
 {
     float xVertex = originalVertex.x;//* 1
     float xVertex_T = originalVertex.x * frameMultX;//both are originalVertex.x * (1 + frameMultX * t)

     //1 is original scale. frameMultX is how much it changes to reach its end scale, in this case 1 since it goes from 1 to 2.

     Vector3 movementX = transform.right * xVertex;
     Vector3 movementX_T = transform.right * xVertex_T;//Get that relative to the object´s rotation.

     Vector3 movementY = transform.up * originalVertex.y;//y axis doesn´t change.

     //Now here is the problem. With Z is the same as X, but  dividing to get the curve: WE ARE WRITING ONLY THE FIRST PART and, once we know for sure the value of t, we do the rest to get the full number: 
     float incompleteMove_Z = transform.forward * originalVertex.z; // / (1 + frameMultX * t) 

     float curveEquation = transform.position + movementX + movementY;
     float curveEquation_T = movementX_T;

     //final equation = curveEquation + curveEquation_T * t + incompleteMove_Z / (1 + frameMultX * t);
 }

All of this is the movement of a vertex from its start position to its end. So basically I have an object that´s being squeezed, incresing its x scale and reducing ts z scale while keeping a constant area.

So I went from this: Vector3 + Vector3 t;
To this: Vector3 + Vector3 t + Vector3 / (1 + float * t);

It works; but because am doing a lot of dot products and other stuff with those equations, this becomes longer and longer and results in cubic, quatric and quintic equations sometimes (which involve a lot of hard calculations), so keeping this structure is not an option.

...My question is, is there a way of getting another equation with the same result, but skipping the division?

I know that (1 + frameMultX t) is the current scale on the x axis. And I know that 1 / (1 + frameMultX t) is the current scale on the z axis, because the scale area divided by the scale on one axis gives the scale on the other axis. But all of this leads to the same. I always end up dividing by a linear equation, which is what causes the problem.

I also tried applying the same principle on the other axis, which is 1 + frameMultZ itsRelativeT; itsRelativet is: (1 / (1 + frameMultX t) - 1) / frameMultZ; But as you can see, it has the same problem.

I was thinking of finding a way of getting this that doesn´t involve dividing the area by the opposite axis, but I can´t find a pattern. I know, for example, that if t = 0.5 , then the scale on x is 1.5 and z is 0.6666. Again, x goes from 1 to 2 and z from 1 to 0.5, so x has advanzed its half and z two thirds.

Thanks in advance.