Simplify (9x^4-6x^3+4x^2)/(27x^4+8x)

$\frac{9 x^{4} - 6 x^{3} + 4 x^{2}}{27 x^{4} + 8 x}$

Factor $x^{2}$ out of $9 x^{4} - 6 x^{3} + 4 x^{2}$ .

Factor $x^{2}$ out of $9 x^{4}$ .

$\frac{x^{2} (9 x^{2}) - 6 x^{3} + 4 x^{2}}{27 x^{4} + 8 x}$

Factor $x^{2}$ out of $- 6 x^{3}$ .

$\frac{x^{2} (9 x^{2}) + x^{2} (- 6 x) + 4 x^{2}}{27 x^{4} + 8 x}$

Factor $x^{2}$ out of $4 x^{2}$ .

$\frac{x^{2} (9 x^{2}) + x^{2} (- 6 x) + x^{2} \cdot 4}{27 x^{4} + 8 x}$

Factor $x^{2}$ out of $x^{2} (9 x^{2}) + x^{2} (- 6 x)$ .

$\frac{x^{2} (9 x^{2} - 6 x) + x^{2} \cdot 4}{27 x^{4} + 8 x}$

Factor $x^{2}$ out of $x^{2} (9 x^{2} - 6 x) + x^{2} \cdot 4$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{27 x^{4} + 8 x}$

Simplify the denominator.

Factor $x$ out of $27 x^{4} + 8 x$ .

Factor $x$ out of $27 x^{4}$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x (27 x^{3}) + 8 x}$

Factor $x$ out of $8 x$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x (27 x^{3}) + x \cdot 8}$

Factor $x$ out of $x (27 x^{3}) + x \cdot 8$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x (27 x^{3} + 8)}$

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ({(3 x)}^{3} + 8)}$

Rewrite $8$ as $2^{3}$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ({(3 x)}^{3} + 2^{3})}$

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 3 x$ and $b = 2$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ((3 x + 2) ({(3 x)}^{2} - (3 x) \cdot 2 + 2^{2}))}$

Simplify.

Apply the product rule to $3 x$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ((3 x + 2) (3^{2} x^{2} - (3 x) \cdot 2 + 2^{2}))}$

Raise $3$ to the power of $2$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ((3 x + 2) (9 x^{2} - (3 x) \cdot 2 + 2^{2}))}$

Multiply $3$ by $- 1$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ((3 x + 2) (9 x^{2} - 3 x \cdot 2 + 2^{2}))}$

Multiply $2$ by $- 3$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ((3 x + 2) (9 x^{2} - 6 x + 2^{2}))}$

Raise $2$ to the power of $2$ .

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x ((3 x + 2) (9 x^{2} - 6 x + 4))}$

$\frac{x^{2} (9 x^{2} - 6 x + 4)}{x (3 x + 2) (9 x^{2} - 6 x + 4)}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $x^{2} (9 x^{2} - 6 x + 4)$ .

$\frac{x (x (9 x^{2} - 6 x + 4))}{x (3 x + 2) (9 x^{2} - 6 x + 4)}$

Cancel the common factors.

Factor $x$ out of $x (3 x + 2) (9 x^{2} - 6 x + 4)$ .

$\frac{x (x (9 x^{2} - 6 x + 4))}{x ((3 x + 2) (9 x^{2} - 6 x + 4))}$

Cancel the common factor.

$\frac{x (x (9 x^{2} - 6 x + 4))}{x ((3 x + 2) (9 x^{2} - 6 x + 4))}$

Rewrite the expression.

$\frac{x (9 x^{2} - 6 x + 4)}{(3 x + 2) (9 x^{2} - 6 x + 4)}$

Cancel the common factor of $9 x^{2} - 6 x + 4$ .

Cancel the common factor.

$\frac{x (9 x^{2} - 6 x + 4)}{(3 x + 2) (9 x^{2} - 6 x + 4)}$

Rewrite the expression.

$\frac{x}{3 x + 2}$

Simplify (9x^4-6x^3+4x^2)/(27x^4+8x)

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