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.