Simplify (-3x^2+13x-12)/(2x^2-x-15)

$\frac{- 3 x^{2} + 13 x - 12}{2 x^{2} - x - 15}$

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 $a \cdot c = - 3 \cdot - 12 = 36$ and whose sum is $b = 13$ .

Factor $13$ out of $13 x$ .

$\frac{- 3 x^{2} + 13 (x) - 12}{2 x^{2} - x - 15}$

Rewrite $13$ as $4$ plus $9$

$\frac{- 3 x^{2} + (4 + 9) x - 12}{2 x^{2} - x - 15}$

Apply the distributive property.

$\frac{- 3 x^{2} + 4 x + 9 x - 12}{2 x^{2} - x - 15}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(- 3 x^{2} + 4 x) + 9 x - 12}{2 x^{2} - x - 15}$

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

$\frac{x (- 3 x + 4) - 3 (- 3 x + 4)}{2 x^{2} - x - 15}$

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

$\frac{(- 3 x + 4) (x - 3)}{2 x^{2} - x - 15}$

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 $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$\frac{(- 3 x + 4) (x - 3)}{2 x^{2} - (x) - 15}$

Rewrite $- 1$ as $5$ plus $- 6$

$\frac{(- 3 x + 4) (x - 3)}{2 x^{2} + (5 - 6) x - 15}$

Apply the distributive property.

$\frac{(- 3 x + 4) (x - 3)}{2 x^{2} + 5 x - 6 x - 15}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(- 3 x + 4) (x - 3)}{(2 x^{2} + 5 x) - 6 x - 15}$

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

$\frac{(- 3 x + 4) (x - 3)}{x (2 x + 5) - 3 (2 x + 5)}$

Factor the polynomial by factoring out the greatest common factor, $2 x + 5$ .

$\frac{(- 3 x + 4) (x - 3)}{(2 x + 5) (x - 3)}$

Step 3

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{(- 3 x + 4) (x - 3)}{(2 x + 5) (x - 3)}$

Rewrite the expression.

$\frac{- 3 x + 4}{2 x + 5}$

Step 4

Factor $- 1$ out of $- 3 x$ .

$\frac{- (3 x) + 4}{2 x + 5}$

Step 5

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{- (3 x) - 1 (- 4)}{2 x + 5}$

Step 6

Factor $- 1$ out of $- (3 x) - 1 (- 4)$ .

$\frac{- (3 x - 4)}{2 x + 5}$

Step 7

Simplify the expression.

Rewrite $- (3 x - 4)$ as $- 1 (3 x - 4)$ .

$\frac{- 1 (3 x - 4)}{2 x + 5}$

Move the negative in front of the fraction.

$- \frac{3 x - 4}{2 x + 5}$

Simplify (-3x^2+13x-12)/(2x^2-x-15)

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