Simplify x/(x^2+4x-45)*(x^2+13x+36)/(x+4)

$\frac{x}{x^{2} + 4 x - 45} \cdot \frac{x^{2} + 13 x + 36}{x + 4}$

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.

$\frac{x}{(x - 5) (x + 9)} \cdot \frac{x^{2} + 13 x + 36}{x + 4}$

Step 2

Factor $x^{2} + 13 x + 36$ 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 $36$ and whose sum is $13$ .

$4, 9$

Write the factored form using these integers.

$\frac{x}{(x - 5) (x + 9)} \cdot \frac{(x + 4) (x + 9)}{x + 4}$

Step 3

Simplify terms.

Cancel the common factor of $x + 9$ .

Factor $x + 9$ out of $(x - 5) (x + 9)$ .

$\frac{x}{(x + 9) (x - 5)} \cdot \frac{(x + 4) (x + 9)}{x + 4}$

Factor $x + 9$ out of $(x + 4) (x + 9)$ .

$\frac{x}{(x + 9) (x - 5)} \cdot \frac{(x + 9) (x + 4)}{x + 4}$

Cancel the common factor.

$\frac{x}{(x + 9) (x - 5)} \cdot \frac{(x + 9) (x + 4)}{x + 4}$

Rewrite the expression.

$\frac{x}{x - 5} \cdot \frac{x + 4}{x + 4}$

Multiply $\frac{x}{x - 5}$ by $\frac{x + 4}{x + 4}$ .

$\frac{x (x + 4)}{(x - 5) (x + 4)}$

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{x (x + 4)}{(x - 5) (x + 4)}$

Rewrite the expression.

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

Simplify x/(x^2+4x-45)*(x^2+13x+36)/(x+4)

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