Find the Excluded Values (k^2-k-2)/(k^2-4k-5)

$\frac{k^{2} - k - 2}{k^{2} - 4 k - 5}$

Set the denominator in $\frac{k^{2} - k - 2}{k^{2} - 4 k - 5}$ equal to $0$ to find where the expression is undefined.

$k^{2} - 4 k - 5 = 0$

Solve for $k$ .

Factor $k^{2} - 4 k - 5$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 5$ and whose sum is $- 4$ .

$- 5, 1$

Write the factored form using these integers.

$(k - 5) (k + 1) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$k - 5 = 0$

$k + 1 = 0$

Set $k - 5$ equal to $0$ and solve for $k$ .

Set $k - 5$ equal to $0$ .

$k - 5 = 0$

Add $5$ to both sides of the equation.

$k = 5$

Set $k + 1$ equal to $0$ and solve for $k$ .

Set $k + 1$ equal to $0$ .

$k + 1 = 0$

Subtract $1$ from both sides of the equation.

$k = - 1$

The final solution is all the values that make $(k - 5) (k + 1) = 0$ true.

$k = 5, - 1$

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$k = - 1, k = 5$

Find the Excluded Values (k^2-k-2)/(k^2-4k-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.