Simplify (9x^2+81x)/(x^3+8x^2-9x)

$\frac{9 x^{2} + 81 x}{x^{3} + 8 x^{2} - 9 x}$

Step 1

Factor $9 x$ out of $9 x^{2} + 81 x$ .

Factor $9 x$ out of $9 x^{2}$ .

$\frac{9 x (x) + 81 x}{x^{3} + 8 x^{2} - 9 x}$

Factor $9 x$ out of $81 x$ .

$\frac{9 x (x) + 9 x (9)}{x^{3} + 8 x^{2} - 9 x}$

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

$\frac{9 x (x + 9)}{x^{3} + 8 x^{2} - 9 x}$

Step 2

Simplify the denominator.

Factor $x$ out of $x^{3} + 8 x^{2} - 9 x$ .

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

$\frac{9 x (x + 9)}{x \cdot x^{2} + 8 x^{2} - 9 x}$

Factor $x$ out of $8 x^{2}$ .

$\frac{9 x (x + 9)}{x \cdot x^{2} + x (8 x) - 9 x}$

Factor $x$ out of $- 9 x$ .

$\frac{9 x (x + 9)}{x \cdot x^{2} + x (8 x) + x \cdot - 9}$

Factor $x$ out of $x \cdot x^{2} + x (8 x)$ .

$\frac{9 x (x + 9)}{x (x^{2} + 8 x) + x \cdot - 9}$

Factor $x$ out of $x (x^{2} + 8 x) + x \cdot - 9$ .

$\frac{9 x (x + 9)}{x (x^{2} + 8 x - 9)}$

Factor $x^{2} + 8 x - 9$ 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 $8$ .

$- 1, 9$

Write the factored form using these integers.

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

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 9$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{9}{x - 1}$

Simplify (9x^2+81x)/(x^3+8x^2-9x)

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