How do you solve #(x-2)/6=(x-2)/(x-1)#?

You carry out multiplication by cross.

that is,

additional simplification

transferring all data to the left side;

reduce to brackets

(x-2) (x - 7)

thus the answers are:

x = 2 and x = 7

:)

To solve the equation (x-2)/6=(x-2)/(x-1), we can start by multiplying both sides of the equation by 6(x-1) to eliminate the denominators. This gives us (x-2)(x-1) = 6(x-2). Expanding and simplifying, we get x^2 - 3x + 2 = 6x - 12. Rearranging the terms, we have x^2 - 9x + 14 = 0. Factoring or using the quadratic formula, we find that x = 7 or x = 2. However, we need to check if these solutions satisfy the original equation. Substituting x = 7, we get (7-2)/6 = (7-2)/(7-1), which simplifies to 1 = 1, so it is a valid solution. Substituting x = 2, we get (2-2)/6 = (2-2)/(2-1), which simplifies to 0 = 0, so it is also a valid solution. Therefore, the solutions to the equation are x = 7 and x = 2.