Simplify (x^2+11x+18)/(5-x)(x^2-2x-15)/(x^2+12x+27)(x^2+x-72)/(x^2+x-72)

$\frac{x^{2} + 11 x + 18}{5 - x} \cdot \frac{x^{2} - 2 x - 15}{x^{2} + 12 x + 27} \cdot \frac{x^{2} + x - 72}{x^{2} + x - 72}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{2} + x - 72$ .

Cancel the common factor.

$\frac{x^{2} + 11 x + 18}{5 - x} \cdot \frac{x^{2} - 2 x - 15}{x^{2} + 12 x + 27} \cdot \frac{x^{2} + x - 72}{x^{2} + x - 72}$

Rewrite the expression.

$\frac{x^{2} + 11 x + 18}{5 - x} \cdot \frac{x^{2} - 2 x - 15}{x^{2} + 12 x + 27} \cdot 1$

Multiply $\frac{x^{2} + 11 x + 18}{5 - x} \cdot \frac{x^{2} - 2 x - 15}{x^{2} + 12 x + 27}$ by $1$ .

$\frac{x^{2} + 11 x + 18}{5 - x} \cdot \frac{x^{2} - 2 x - 15}{x^{2} + 12 x + 27}$

Factor $x^{2} + 11 x + 18$ 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 $18$ and whose sum is $11$ .

$2, 9$

Write the factored form using these integers.

$\frac{(x + 2) (x + 9)}{5 - x} \cdot \frac{x^{2} - 2 x - 15}{x^{2} + 12 x + 27}$

Factor $x^{2} - 2 x - 15$ 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 $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Write the factored form using these integers.

$\frac{(x + 2) (x + 9)}{5 - x} \cdot \frac{(x - 5) (x + 3)}{x^{2} + 12 x + 27}$

Factor $x^{2} + 12 x + 27$ 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 $27$ and whose sum is $12$ .

$3, 9$

Write the factored form using these integers.

$\frac{(x + 2) (x + 9)}{5 - x} \cdot \frac{(x - 5) (x + 3)}{(x + 3) (x + 9)}$

Simplify terms.

Cancel the common factor of $x + 9$ .

Factor $x + 9$ out of $(x + 2) (x + 9)$ .

$\frac{(x + 9) (x + 2)}{5 - x} \cdot \frac{(x - 5) (x + 3)}{(x + 3) (x + 9)}$

Factor $x + 9$ out of $(x + 3) (x + 9)$ .

$\frac{(x + 9) (x + 2)}{5 - x} \cdot \frac{(x - 5) (x + 3)}{(x + 9) (x + 3)}$

Cancel the common factor.

$\frac{(x + 9) (x + 2)}{5 - x} \cdot \frac{(x - 5) (x + 3)}{(x + 9) (x + 3)}$

Rewrite the expression.

$\frac{x + 2}{5 - x} \cdot \frac{(x - 5) (x + 3)}{x + 3}$

Simplify terms.

Multiply $\frac{x + 2}{5 - x}$ by $\frac{(x - 5) (x + 3)}{x + 3}$ .

$\frac{(x + 2) ((x - 5) (x + 3))}{(5 - x) (x + 3)}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(x + 2) ((x - 5) (x + 3))}{(5 - x) (x + 3)}$

Rewrite the expression.

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

Cancel the common factor of $x - 5$ and $5 - x$ .

Factor $- 1$ out of $x$ .

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

Rewrite $- 5$ as $- 1 (5)$ .

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

Factor $- 1$ out of $- 1 (- x) - 1 (5)$ .

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

Reorder terms.

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

Cancel the common factor.

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

Divide $(x + 2) \cdot (- 1)$ by $1$ .

$(x + 2) \cdot (- 1)$

Apply the distributive property.

$x \cdot - 1 + 2 \cdot - 1$

Simplify the expression.

Move $- 1$ to the left of $x$ .

$- 1 \cdot x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$- 1 \cdot x - 2$

Rewrite $- 1 x$ as $- x$ .

$- x - 2$

Simplify (x^2+11x+18)/(5-x)*(x^2-2x-15)/(x^2+12x+27)*(x^2+x-72)/(x^2+x-72)

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Simplify (x^2+11x+18)/(5-x)(x^2-2x-15)/(x^2+12x+27)(x^2+x-72)/(x^2+x-72)