Simplify (x^3+11x^2+18x)/(x^2+x-2)

$\frac{x^{3} + 11 x^{2} + 18 x}{x^{2} + x - 2}$

Step 1

Simplify the numerator.

Factor $x$ out of $x^{3} + 11 x^{2} + 18 x$ .

Factor $x$ out of $x^{3}$ .

$\frac{x \cdot x^{2} + 11 x^{2} + 18 x}{x^{2} + x - 2}$

Factor $x$ out of $11 x^{2}$ .

$\frac{x \cdot x^{2} + x (11 x) + 18 x}{x^{2} + x - 2}$

Factor $x$ out of $18 x$ .

$\frac{x \cdot x^{2} + x (11 x) + x \cdot 18}{x^{2} + x - 2}$

Factor $x$ out of $x \cdot x^{2} + x (11 x)$ .

$\frac{x (x^{2} + 11 x) + x \cdot 18}{x^{2} + x - 2}$

Factor $x$ out of $x (x^{2} + 11 x) + x \cdot 18$ .

$\frac{x (x^{2} + 11 x + 18)}{x^{2} + x - 2}$

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.

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

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

Step 2

Factor $x^{2} + x - 2$ 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 $1$ .

$- 1, 2$

Write the factored form using these integers.

$\frac{x (x + 2) (x + 9)}{(x - 1) (x + 2)}$

Step 3

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{x (x + 2) (x + 9)}{(x - 1) (x + 2)}$

Rewrite the expression.

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

Simplify (x^3+11x^2+18x)/(x^2+x-2)

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