Simplify (2x^3+x^2-3x)/(3x^2-5x+2)

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

Simplify the numerator.

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

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

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

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

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

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

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

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

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

Factor $x$ out of $x (2 x^{2} + x) + x \cdot - 3$ .

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

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = 1$ .

Multiply by $1$ .

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

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

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

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 $a \cdot c = 3 \cdot 2 = 6$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 x$ .

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

Rewrite $- 5$ as $- 2$ plus $- 3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (2x^3+x^2-3x)/(3x^2-5x+2)

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