Simplify (x^2-4x-5)/(x^2+6x+5)

$\frac{x^{2} - 4 x - 5}{x^{2} + 6 x + 5}$

Step 1

Factor $x^{2} - 4 x - 5$ 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.

$\frac{(x - 5) (x + 1)}{x^{2} + 6 x + 5}$

Step 2

Factor $x^{2} + 6 x + 5$ 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 $6$ .

$1, 5$

Write the factored form using these integers.

$\frac{(x - 5) (x + 1)}{(x + 1) (x + 5)}$

Step 3

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{(x - 5) (x + 1)}{(x + 1) (x + 5)}$

Rewrite the expression.

$\frac{x - 5}{x + 5}$

Simplify (x^2-4x-5)/(x^2+6x+5)

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