2b-2/2b^2-8 (find domain to rational expression)

I bet you meant:

(2b - 2)/(2b^2 - 8)
= 2(b-1)/(2(b^2- 4))
= (b-1)/((b+2)(b-2))

domain, any real value of b, b ≠ ± 2

range: any real value

see:
graph of y = (x-1)/(x^2 - 4)

http://www.wolframalpha.com/input/?i=y+%3D+%28x-1%29%2F%28x%5E2+-+4%29+from+-5+to+5

notice the two verticals are the asymptotes and should be dotted lines

To find the domain of a rational expression, we need to identify any values for which the expression is undefined.

In this case, the expression is defined for all values of 'b' except those that make the denominator equal to zero.

So, to find the domain of the rational expression 2b-2 / 2b^2-8, we need to set the denominator equal to zero and solve for 'b'.

2b^2 - 8 = 0

First, let's factor out the common factor of 2:
2(b^2 - 4) = 0

Now, we have a difference of squares:
2(b - 2)(b + 2) = 0

To find the values of 'b' that make the expression undefined, we set each factor equal to zero:

b - 2 = 0 --> b = 2
b + 2 = 0 --> b = -2

So, the expression is undefined when 'b' is equal to 2 or -2.

Therefore, the domain of the rational expression 2b-2 / 2b^2-8 is all real numbers except for b = 2 and b = -2.