Simplify the rational expressions.State any excluded values:(1).3x-6/x-2

(2).x-2/x^2+3x-10

I think the first one is

(3x-6)/(x-2)

factor out 3(x-2)/(x-2)
Your answer is 3

(x-2)/(x^2 +3x-10)

factor the denominator... I would guess that (x-2) might be one of the factors so we could simplify..
It is... (x-2)(x+5)

1/(x+5)

A denominator can never equal zero. Exclude any values that will make a denominator zero.

Idek what this is I'm so confused..

I don't have no idea why you guys post this thing with no-understanding .

Sorry because I am not smart enough !!!

More than confused .

To simplify the given rational expressions, we need to simplify the numerator and denominator separately and then express the resulting expression in its simplest form.

(1) Simplifying the rational expression (3x - 6) / (x - 2):

To simplify the numerator, we can factor out a common factor which is 3: 3(x - 2).
And the denominator (x - 2) does not have any common factors to simplify.

Therefore, the simplified expression is 3(x - 2) / (x - 2 ).

Now, let's look at the excluded values.

Excluded values refer to the values of x that make the denominator equal to zero since division by zero is undefined. In this case, the denominator (x - 2) should not be equal to zero.

Let's solve the equation x - 2 = 0 to find the excluded value:
x - 2 = 0
x = 2

So, the excluded value is x = 2.

Therefore, the simplified expression is 3(x - 2) / (x - 2), with the excluded value x = 2.

(2) Simplifying the rational expression (x - 2) / (x^2 + 3x - 10):

To simplify the numerator, we don't have any common factors to remove.
And for the denominator, we can factorize it as follows: (x - 2)(x + 5).

So, the simplified expression is (x - 2) / (x - 2)(x + 5).

Now, let's determine the excluded values.

We need to find the values of x that make the denominator (x - 2)(x + 5) equal to zero.

To do this, we set each factor equal to zero and solve for x:

For (x - 2) = 0, adding 2 to both sides:
x - 2 = 0
x = 2

For (x + 5) = 0, subtracting 5 from both sides:
x + 5 = 0
x = -5

So, the excluded values are x = 2 and x = -5.

Therefore, the simplified expression is (x - 2) / (x - 2)(x + 5), with the excluded values x = 2 and x = -5.