Final answer:
The expression y=(2xy)/(6x²-8x) simplifies to y=0 when x is not equal to 2, and it is undefined when x=2 after cancelling the common x factor and completing the simplification steps.
Step-by-step explanation:
To simplify the expression y=(2xy)/(6x²-8x), we look for common factors in the numerator and denominator. First, factor out an x from the denominator: 6x²-8x = 2x(3x-4). Now, we can see that there is an x in both the numerator and the denominator which can be cancelled out. This leaves us with y = 2y / (3x - 4). To solve for y, we perform cross-multiplication yielding y(3x - 4) = 2y. By distributing y on the left side, we get 3xy - 4y = 2y. To isolate y, move all y terms to one side: 3xy - 6y = 0 which simplifies to y(3x - 6) = 0. This implies y can only be zero for the equation to hold true since 3x - 6 could be non-zero for most values of x except for x = 2. Therefore, the simplified form of the original expression is y = 0 if x ≠ 2 and undefined for x = 2.