Simplify (x^3+x^2y-6xy^2)/(x^2-2xy)

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

Simplify the numerator.

Factor $x$ out of $x^{3} + x^{2} y - 6 x y^{2}$ .

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

$\frac{x \cdot x^{2} + x^{2} y - 6 x y^{2}}{x^{2} - 2 x y}$

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

$\frac{x \cdot x^{2} + x (x y) - 6 x y^{2}}{x^{2} - 2 x y}$

Factor $x$ out of $- 6 x y^{2}$ .

$\frac{x \cdot x^{2} + x (x y) + x (- 6 y^{2})}{x^{2} - 2 x y}$

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

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

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

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

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

Reorder terms.

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

Reorder $- 6 y^{2}$ and $x y$ .

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

Factor $1$ out of $x y$ .

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

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

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

Apply the distributive property.

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

Move parentheses.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

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

Simplify terms.

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

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

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

Factor $x$ out of $- 2 x y$ .

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

Factor $x$ out of $x \cdot x + x (- 2 y)$ .

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 2 y$ .

Cancel the common factor.

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

Divide $x + 3 y$ by $1$ .

$x + 3 y$

Simplify (x^3+x^2y-6xy^2)/(x^2-2xy)

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