1. Simplify the rational expression State any excluded values.

7x-14/x-2

A.x
B.7;where x≠7
C.7;where x≠2****
D.0

I know its between B and C but I'm not sure what the -->≠ is really asking me for but I think the answer is C, please help

it is clearly C, because

(7x-14) = 7(x-2)

but you cannot have a denominator of zero. So, while the fraction is equal to 7 almost everywhere, the value of x=2 is excluded because then the fraction is

7(0)/0 and is undefined.

The numerator can be zero whenever it wants, so x=7 is perfectly ok.

7(0)/5 = 0

and is just fine.

Well, it looks like you're in for a fun explanation! The symbol "≠" means "does not equal to." So, when it says x≠2, it means that x cannot be equal to 2.

Now let's get back to the rational expression. We have 7x - 14 over x - 2. To simplify this expression, we can factor out a common factor of 7 from the numerator:

7(x - 2) / (x - 2)

Now, we can cancel out the common factor of x - 2 from the numerator and denominator, which leaves us with:

7

Ta-da! The simplified rational expression is just 7. So, the answer is indeed C, with the excluded value being x≠2. And remember, don't try to be 2 cool for school!

The symbol "≠" means "not equal to." In this context, it is asking for any values of x that would make the expression undefined.

To simplify the rational expression 7x - 14 / x - 2, we can factor the numerator and denominator if possible. The numerator can be factored as 7(x - 2), but the denominator cannot be factored further.

So, the simplified expression becomes 7(x - 2) / (x - 2).

Now, we can see that the factor (x - 2) appears both in the numerator and denominator. This means that (x - 2) is a common factor and can be canceled out.

When canceling out common factors, we need to consider the excluded values - the values of x that would make the denominator zero. Since the denominator is x - 2, the excluded value is x = 2, as division by zero is undefined.

Therefore, the simplified rational expression is 7, with the excluded value of x = 2.

Hence, the correct answer is C.

To simplify the rational expression (7x - 14) / (x - 2), we need to simplify the numerator and the denominator individually, and then simplify the resulting expression.

First, let's factor the numerator:
7x - 14 = 7(x - 2)

Now, let's simplify the denominator:
x - 2

Next, we can simplify the expression (7x - 14) / (x - 2) by canceling out the common factor of 7 in the numerator and the denominator, which gives us:
7(x - 2) / (x - 2)

The (x - 2) term in the numerator and the denominator can be canceled out, as long as x ≠ 2. That's because if x is equal to 2, the denominator becomes zero, and division by zero is undefined.

Therefore, the excluded value for x is 2, indicated by the restriction x ≠ 2.

Hence, the simplified rational expression with the excluded value is option C: 7; where x ≠ 2.