Final answer:
The expression (2x3-14x2)/(6x-42) can be simplified to x2/3 by factoring out common factors from both the numerator and the denominator and then canceling them out.
Step-by-step explanation:
To simplify the expression (2x3-14x2)/(6x-42), you need to recognize that both the numerator and the denominator have common factors, which you can divide by to simplify the expression. Let's start with the numerator:
- Factor out 2x2 from each term: 2x2(x-7).
- Now let's look at the denominator: Factor out 6 from each term: 6(x-7).
After factoring, you get 2x2(x-7)/6(x-7). You can see that (x-7) is a common factor on the numerator and denominator, so you can cancel it out.
The simplest form of the expression is: 2x2/6, or x2/3 when it's simplified further. In fact, this is the same result regardless if x equals 7 or not.
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