Given Information:
We are given two points: A(2, 1, 3) and B(4, -2, 5) and a plane equation: 2x - y - z = 3.

Approach:
To find the ratio in which the plane divides the line joining the two given points, we can follow these steps:
1. Find the equation of the line passing through points A and B.
2. Substitute the equation of the line into the plane equation to find the point of intersection.
3. Calculate the distances between the points of intersection and the given points A and B.
4. Find the ratio of these distances.

Calculation:
1. Finding the equation of the line passing through points A and B:
The equation of a line passing through two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by:
(x - x₁)/(x₂ - x₁) = (y - y₁)/(y₂ - y₁) = (z - z₁)/(z₂ - z₁)

Substituting the given points A(2, 1, 3) and B(4, -2, 5) into the equation, we get:
(x - 2)/(4 - 2) = (y - 1)/(-2 - 1) = (z - 3)/(5 - 3)
(x - 2)/2 = (y - 1)/(-3) = (z - 3)/2

Simplifying the equation, we get:
3(x - 2) = -2(y - 1) = 2(z - 3)
3x - 6 = -2y + 2 = 2z - 6

Rearranging the terms, we get the equation of the line:
3x + 2y - 2z = -2

2. Substituting the equation of the line into the plane equation to find the point of intersection:
We need to solve the system of equations formed by the line equation and the plane equation.
We have:
2x - y - z = 3 (Plane equation)
3x + 2y - 2z = -2 (Line equation)

Solving these equations, we find the point of intersection:
Multiplying the plane equation by 2, we get:
4x - 2y - 2z = 6

Adding this equation to the line equation, we eliminate the y and z terms:
(3x + 4x) + (2y - 2y) + (-2z - 2z) = (-2 + 6)
7x = 4
x = 4/7

Substituting the value of x into the plane equation, we can find the values of y and z:
2(4/7) - y - z = 3
8/7 - y - z = 3
-y - z = 3 - 8/7
-y - z = 17/7

Since there are two variables and only one equation