Question

X+3/3x+6 multiply x^2+4x-2/x^2+4x+3

Simplify

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify, we can first factor the numerator and denominator of the expression.

Numerator: x^2 + 4x - 2
This trinomial cannot be factored further.

Denominator: x^2 + 4x + 3
This trinomial can be factored as (x + 1)(x + 3).

So, the simplified expression becomes:

(x + 3/3x + 6) * (x^2 + 4x - 2/x^2 + 4x + 3)
= (x + 3/3(x + 2)) * (x^2 + 4x - 2/(x + 1)(x + 3))
= (x + 3(x + 1) * (x - 2)/(x + 1)(x + 3))

Now, we can cancel out the common factors:

= (x + 3) * (x - 2)/(x + 3)
= (x - 2)

So, the simplified expression is x - 2.

Answer 2

so many mistakes!

(x+3)/(3x+6) * (x^2+4x-2)/(x^2+4x+3)
= (x+3)/(3(x+2)) * (x^2+4x-2)/((x+1)(x+3))
= (x^2+4x-2)/(3(x+1)(x+2))

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistakes in my previous response.

The correct simplification of the expression is:

(x+3)/(3x+6) * (x^2 + 4x - 2)/(x^2 + 4x + 3)
= (x+3)/(3(x+2)) * (x^2 + 4x - 2)/((x+1)(x+3))
= (x^2 + 4x - 2)/(3(x+1)(x+2))