Simplify (x^2+4x-45)/(x^2+10x+9)

$\frac{x^{2} + 4 x - 45}{x^{2} + 10 x + 9}$

Step 1

Factor $x^{2} + 4 x - 45$ 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 $- 45$ and whose sum is $4$ .

$- 5, 9$

Write the factored form using these integers.

$\frac{(x - 5) (x + 9)}{x^{2} + 10 x + 9}$

Step 2

Factor $x^{2} + 10 x + 9$ 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 $9$ and whose sum is $10$ .

$1, 9$

Write the factored form using these integers.

$\frac{(x - 5) (x + 9)}{(x + 1) (x + 9)}$

Step 3

Cancel the common factor of $x + 9$ .

Cancel the common factor.

$\frac{(x - 5) (x + 9)}{(x + 1) (x + 9)}$

Rewrite the expression.

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

Simplify (x^2+4x-45)/(x^2+10x+9)

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