Simplify (6x^2+x-12)/(2x+3)

$\frac{6 x^{2} + x - 12}{2 x + 3}$

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 $a \cdot c = 6 \cdot - 12 = - 72$ and whose sum is $b = 1$ .

Multiply by $1$ .

$\frac{6 x^{2} + 1 x - 12}{2 x + 3}$

Rewrite $1$ as $- 8$ plus $9$

$\frac{6 x^{2} + (- 8 + 9) x - 12}{2 x + 3}$

Apply the distributive property.

$\frac{6 x^{2} - 8 x + 9 x - 12}{2 x + 3}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 x^{2} - 8 x) + 9 x - 12}{2 x + 3}$

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

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

Factor the polynomial by factoring out the greatest common factor, $3 x - 4$ .

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

Cancel the common factor of $2 x + 3$ .

Cancel the common factor.

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

Divide $3 x - 4$ by $1$ .

$3 x - 4$

Simplify (6x^2+x-12)/(2x+3)

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