Add the rational expressions to find the sum: −4x−4+x2−2x2x−8. Put the answer into its simplest form.

Question

Responses

x2−2x−4x−4
the fraction with numerator x squared minus 2 x minus 4 and denominator x minus 4 - incorrect

x2−2x−82x−8
the fraction with numerator x squared minus 2 x minus 8 and denominator 2 x minus 8 - no response given

x+22
the fraction with numerator x plus 2 and denominator 2 -this is the correct answer

x2−2x2x
explain how you would get that as x+2/2 in your correct answer.

Answer 1

To simplify the given rational expression, we need to combine like terms.

The given expression is: -4x - 4 + x^2 - 2x / (2x - 8)

Combining like terms, we have: (x^2 - 4x - 4 - 2x) / (2x - 8)

Simplifying further, we have: (x^2 - 6x - 4) / (2x - 8)

Factoring the numerator, we have: [(x - 2)(x + 2)] / (2x - 8)

Now, we can see that (x + 2) is a common factor in both the numerator and denominator, and we can cancel it out.

The final simplified answer is: (x - 2) / 2