Simplify (k^2-k-2)/(k^2-4k-5)

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

Step 1

Factor $k^{2} - k - 2$ 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 $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Write the factored form using these integers.

$\frac{(k - 2) (k + 1)}{k^{2} - 4 k - 5}$

Step 2

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.

$\frac{(k - 2) (k + 1)}{(k - 5) (k + 1)}$

Step 3

Cancel the common factor of $k + 1$ .

Cancel the common factor.

$\frac{(k - 2) (k + 1)}{(k - 5) (k + 1)}$

Rewrite the expression.

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

Simplify (k^2-k-2)/(k^2-4k-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.