Find the domains of rational expressions
2b-2/2b^2-8
please show steps
(2b-2)/(2b^2-8)
2b^2-8 = 0
2b^2 = 8
b^2 = 4
b=+-2 Gives a denominator of zero which
makes the expression Undefined.
Domain: All real values of b except +2
and -2.
Mathematically: -2 > b > 2.
mathematically, |b| ≠ 2
or b^2 ≠ 4
To find the domain of a rational expression, we need to consider two things:
1. Exclude any values that would make the denominator equal to zero.
2. Exclude any values that would cause the expression to be undefined.
Let's break down the steps to find the domain of the given rational expression:
Step 1: Exclude values that make the denominator zero
The denominator of the rational expression is 2b^2 - 8. Set the denominator equal to zero and solve for b:
2b^2 - 8 = 0
To solve the equation above, add 8 to both sides:
2b^2 = 8
Divide both sides by 2:
b^2 = 4
Now, take the square root of both sides:
b = ±2
So, b cannot equal 2 or -2 because they would make the denominator zero.
Step 2: Check for any other restrictions
In this specific rational expression, there are no other factors or variables involved where the expression could be undefined. Therefore, we do not need to exclude any other values.
Step 3: Conclusion
The domain of the given rational expression, 2b - 2 / 2b^2 - 8, is all real numbers except b = 2 and b = -2. So, the domain can be written as (-∞, -2)U(-2, 2)U(2, ∞).