Simplify (16x^3-16x^2+4x)/(12x^3+12x^2+3x)

$\frac{16 x^{3} - 16 x^{2} + 4 x}{12 x^{3} + 12 x^{2} + 3 x}$

Simplify the numerator.

Tap for more steps…

Factor $4 x$ out of $16 x^{3} - 16 x^{2} + 4 x$ .

Tap for more steps…

Factor $4 x$ out of $16 x^{3}$ .

$\frac{4 x (4 x^{2}) - 16 x^{2} + 4 x}{12 x^{3} + 12 x^{2} + 3 x}$

Factor $4 x$ out of $- 16 x^{2}$ .

$\frac{4 x (4 x^{2}) + 4 x (- 4 x) + 4 x}{12 x^{3} + 12 x^{2} + 3 x}$

Factor $4 x$ out of $4 x$ .

$\frac{4 x (4 x^{2}) + 4 x (- 4 x) + 4 x (1)}{12 x^{3} + 12 x^{2} + 3 x}$

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

$\frac{4 x (4 x^{2} - 4 x) + 4 x (1)}{12 x^{3} + 12 x^{2} + 3 x}$

Factor $4 x$ out of $4 x (4 x^{2} - 4 x) + 4 x (1)$ .

$\frac{4 x (4 x^{2} - 4 x + 1)}{12 x^{3} + 12 x^{2} + 3 x}$

Factor using the perfect square rule.

Tap for more steps…

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\frac{4 x ({(2 x)}^{2} - 4 x + 1)}{12 x^{3} + 12 x^{2} + 3 x}$

Rewrite $1$ as $1^{2}$ .

$\frac{4 x ({(2 x)}^{2} - 4 x + 1^{2})}{12 x^{3} + 12 x^{2} + 3 x}$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot (2 x) \cdot - 1$

Simplify.

$2 a b = - 4 x$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 x$ and $b = - 1$ .

$\frac{4 x {(2 x - 1)}^{2}}{12 x^{3} + 12 x^{2} + 3 x}$

Simplify the denominator.

Tap for more steps…

Factor $3 x$ out of $12 x^{3} + 12 x^{2} + 3 x$ .

Tap for more steps…

Factor $3 x$ out of $12 x^{3}$ .

$\frac{4 x {(2 x - 1)}^{2}}{3 x (4 x^{2}) + 12 x^{2} + 3 x}$

Factor $3 x$ out of $12 x^{2}$ .

$\frac{4 x {(2 x - 1)}^{2}}{3 x (4 x^{2}) + 3 x (4 x) + 3 x}$

Factor $3 x$ out of $3 x$ .

$\frac{4 x {(2 x - 1)}^{2}}{3 x (4 x^{2}) + 3 x (4 x) + 3 x (1)}$

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

$\frac{4 x {(2 x - 1)}^{2}}{3 x (4 x^{2} + 4 x) + 3 x (1)}$

Factor $3 x$ out of $3 x (4 x^{2} + 4 x) + 3 x (1)$ .

$\frac{4 x {(2 x - 1)}^{2}}{3 x (4 x^{2} + 4 x + 1)}$

Factor using the perfect square rule.

Tap for more steps…

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\frac{4 x {(2 x - 1)}^{2}}{3 x ({(2 x)}^{2} + 4 x + 1)}$

Rewrite $1$ as $1^{2}$ .

$\frac{4 x {(2 x - 1)}^{2}}{3 x ({(2 x)}^{2} + 4 x + 1^{2})}$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot (2 x) \cdot 1$

Simplify.

$2 a b = 4 x$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2 x$ and $b = 1$ .

$\frac{4 x {(2 x - 1)}^{2}}{3 x {(2 x + 1)}^{2}}$

Cancel the common factor of $x$ .

Tap for more steps…

Cancel the common factor.

$\frac{4 x {(2 x - 1)}^{2}}{3 x {(2 x + 1)}^{2}}$

Rewrite the expression.

$\frac{4 {(2 x - 1)}^{2}}{3 {(2 x + 1)}^{2}}$

Simplify (16x^3-16x^2+4x)/(12x^3+12x^2+3x)