Simplify the rational expression. state any restrictions on the variable. k² - k - 2/k² - 4k - 5

Solution:

Given: Rational expression k² - k - 2/k² - 4k - 5

Consider the expression in the numerator.

Let us factor k² - k - 2.

k² - k - 2 = (k² - 2k + k - 2)

= (k + 1)(k - 2)

Consider the expression in the denominator.

Let us factor k² - 4k - 5.

k² - 4k - 5. = k² - 5k + k - 5

= (k + 1)(k - 5)

Now the given expression is factored as:

[(k + 1)(k - 2)]/[(k + 1)(k - 5)]

=(k - 2)/(k - 5)

For this expression k² - k - 2/k² - 4k - 5 to exist as a real term, k ≠ 5

---

Simplify the rational expression. state any restrictions on the variable. k² - k - 2/k² - 4k - 5

Summary:

The simplified rational expression of k² - k - 2/k² - 4k - 5 is (k - 2)/(k - 5) and restriction on variable is k ≠ 5