Simplify (3x^2+25x+28)/(12x^2+7x-12)

$\frac{3 x^{2} + 25 x + 28}{12 x^{2} + 7 x - 12}$

Step 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 $a \cdot c = 3 \cdot 28 = 84$ and whose sum is $b = 25$ .

Factor $25$ out of $25 x$ .

$\frac{3 x^{2} + 25 (x) + 28}{12 x^{2} + 7 x - 12}$

Rewrite $25$ as $4$ plus $21$

$\frac{3 x^{2} + (4 + 21) x + 28}{12 x^{2} + 7 x - 12}$

Apply the distributive property.

$\frac{3 x^{2} + 4 x + 21 x + 28}{12 x^{2} + 7 x - 12}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(3 x^{2} + 4 x) + 21 x + 28}{12 x^{2} + 7 x - 12}$

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

$\frac{x (3 x + 4) + 7 (3 x + 4)}{12 x^{2} + 7 x - 12}$

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

$\frac{(3 x + 4) (x + 7)}{12 x^{2} + 7 x - 12}$

Step 2

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 $a \cdot c = 12 \cdot - 12 = - 144$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$\frac{(3 x + 4) (x + 7)}{12 x^{2} + 7 (x) - 12}$

Rewrite $7$ as $- 9$ plus $16$

$\frac{(3 x + 4) (x + 7)}{12 x^{2} + (- 9 + 16) x - 12}$

Apply the distributive property.

$\frac{(3 x + 4) (x + 7)}{12 x^{2} - 9 x + 16 x - 12}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(3 x + 4) (x + 7)}{(12 x^{2} - 9 x) + 16 x - 12}$

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

$\frac{(3 x + 4) (x + 7)}{3 x (4 x - 3) + 4 (4 x - 3)}$

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

$\frac{(3 x + 4) (x + 7)}{(4 x - 3) (3 x + 4)}$

Step 3

Cancel the common factor of $3 x + 4$ .

Cancel the common factor.

$\frac{(3 x + 4) (x + 7)}{(4 x - 3) (3 x + 4)}$

Rewrite the expression.

$\frac{x + 7}{4 x - 3}$

Simplify (3x^2+25x+28)/(12x^2+7x-12)

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