Divide (12x^2+2x-2)/(3x-1)

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

Step 1

Simplify the numerator.

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

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

$\frac{2 (6 x^{2}) + 2 x - 2}{3 x - 1}$

Factor $2$ out of $2 x$ .

$\frac{2 (6 x^{2}) + 2 (x) - 2}{3 x - 1}$

Factor $2$ out of $- 2$ .

$\frac{2 (6 x^{2}) + 2 (x) + 2 (- 1)}{3 x - 1}$

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

$\frac{2 (6 x^{2} + x) + 2 (- 1)}{3 x - 1}$

Factor $2$ out of $2 (6 x^{2} + x) + 2 (- 1)$ .

$\frac{2 (6 x^{2} + x - 1)}{3 x - 1}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot - 1 = - 6$ and whose sum is $b = 1$ .

Multiply by $1$ .

$\frac{2 (6 x^{2} + 1 x - 1)}{3 x - 1}$

Rewrite $1$ as $- 2$ plus $3$

$\frac{2 (6 x^{2} + (- 2 + 3) x - 1)}{3 x - 1}$

Apply the distributive property.

$\frac{2 (6 x^{2} - 2 x + 3 x - 1)}{3 x - 1}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{2 ((6 x^{2} - 2 x) + 3 x - 1)}{3 x - 1}$

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

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

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

Step 2

Cancel the common factor of $3 x - 1$ .

Cancel the common factor.

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

Divide $2 (2 x + 1)$ by $1$ .

$2 (2 x + 1)$

Step 3

Apply the distributive property.

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

Step 4

Multiply $2$ by $2$ .

$4 x + 2 \cdot 1$

Step 5

Multiply $2$ by $1$ .

$4 x + 2$

Divide (12x^2+2x-2)/(3x-1)

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