%2F(a%2B1).jpeg "(2a^2-4a-8)/(a+1)")
Simplifying the Expression (2a^2 - 4a - 8) / (a + 1)
This article will guide you through the process of simplifying the rational expression (2a^2 - 4a - 8) / (a + 1).
1. Factoring the Numerator
The first step is to factor the numerator, 2a^2 - 4a - 8. We can factor out a 2 from each term:
2a^2 - 4a - 8 = 2(a^2 - 2a - 4)
Next, we need to factor the quadratic expression inside the parentheses. We can use the quadratic formula or factoring by grouping to find the factors. In this case, the quadratic expression does not factor nicely, so we will leave it as it is.
2. Simplifying the Expression
Now our expression looks like this:
(2a^2 - 4a - 8) / (a + 1) = 2(a^2 - 2a - 4) / (a + 1)
Since there are no common factors between the numerator and denominator, the expression is already in its simplest form.
3. Restrictions on the Variable
It's important to note that the expression is undefined when the denominator is equal to zero. So we need to find the values of 'a' that make the denominator zero:
a + 1 = 0 a = -1
Therefore, the expression is undefined for a = -1.
Conclusion
We have successfully simplified the expression (2a^2 - 4a - 8) / (a + 1) to 2(a^2 - 2a - 4) / (a + 1). We have also identified the restriction on the variable, a ≠ -1.