Question

2u^2-16u+24/u^2+u-6 simplify

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (2u^2 - 16u + 24) / (u^2 + u - 6), we first factor both the numerator and the denominator.

The numerator can be factored as:
2u^2 - 16u + 24 = 2(u^2 - 8u + 12) = 2(u - 2)(u - 6)

The denominator can be factored as:
u^2 + u - 6 = (u + 3)(u - 2)

Now, we can cancel out the common factors:
(2u - 2)(u - 6) / (u + 3)(u - 2)

The (u - 2) terms cancel out, leaving us with:
(2u - 2) / (u + 3)

Simplifying further, we can factor out a 2 from the numerator:
2(u - 1) / (u + 3)

Therefore, the simplified expression is 2(u - 1) / (u + 3).

Answer 2

you cannot factor out a 2 from 2(u-2) to get 2(u-1)

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. You are correct.

Let's go through the simplification process again:

To simplify the expression (2u^2 - 16u + 24) / (u^2 + u - 6), we can start by factoring the numerator and the denominator.

The numerator can be factored as:
2u^2 - 16u + 24 = 2(u^2 - 8u + 12) = 2(u - 2)(u - 6)

The denominator can be factored as:
u^2 + u - 6 = (u + 3)(u - 2)

Now, we can eliminate common factors:
(2(u - 2)(u - 6)) / ((u + 3)(u - 2))

The (u - 2) terms in the numerator and denominator cancel out, leaving us with:
(2(u - 6)) / (u + 3)

Therefore, the simplified expression is 2(u - 6) / (u + 3).