Question

Write each rational expression in simplest form. State all restrictions on the variables

2𝑥^2−2𝑥−12/4𝑥−12

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the rational expression, we can start by factoring the numerator and denominator if possible.

The numerator is 2𝑥^2−2𝑥−12. We can factor out a 2 from each term, which gives us 2(𝑥^2−𝑥−6). Now we need to factor the quadratic expression 𝑥^2−𝑥−6. This can be factored as (𝑥−3)(𝑥+2).

So the numerator can be written as 2(𝑥−3)(𝑥+2).

The denominator is 4𝑥−12 which can be factored out a common factor of 4, giving us 4(𝑥−3).

Now, we can cancel out the common factor of (𝑥−3) in the numerator and denominator:

2(𝑥−3)(𝑥+2)/4(𝑥−3)

Canceling out the common factor, we are left with:

2(𝑥+2)/4

Now we can simplify further. We can simplify the expression 2(𝑥+2) by canceling the common factor of 2:

(𝑥+2)/2

The final simplified form of the rational expression is (𝑥+2)/2, with the restriction that 𝑥 cannot be equal to 3, as that would cause a division by zero in the denominator.