Final answer:
The statement is false because the limit of a rational function cannot be simply split into the limit of the numerator divided by the limit of the denominator, especially when the denominator approaches zero.
Step-by-step explanation:
The statement lim x→1 (x - 5x²)/(2x - 4) = lim x→1 (x - 5) / lim x→1 (x²)/(2x - 4) is false. In the world of limits and rational functions such as the ones presented, it is not always true that a limit of a fraction equals the fraction of the limits. Limits should be evaluated separately and only when both the numerator and denominator limits exist separately and are finite can they be divided as such.
Here, applying direct substitution for x equals 1 in the denominator (2x - 4) would yield 0, indicating a possible indeterminate form. To properly evaluate the limit, we would first need to simplify the expression where possible and then take the limit of the simplified form, if it exists. It's incorrect to divide the numerator and denominator limits when the limit of the denominator is 0 or the expression is in an indeterminate form.