Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

$\frac{x \cdot x - x y}{3 y^{2} - 3 x y}$

Step 1.1.2

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

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

Step 1.1.3

Factor $x$ out of $x \cdot x + x (- 1 y)$ .

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

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

Step 1.2

Rewrite $- 1 y$ as $- y$ .

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

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

Factor $3 y$ out of $3 y (y) + 3 y (- x)$ .

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

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

Step 2.2

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

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Step 2.2.1

Factor $- 1$ out of $x$ .

$\frac{x (- 1 (- x) - y)}{3 y (y - x)}$

Step 2.2.2

Factor $- 1$ out of $- y$ .

$\frac{x (- 1 (- x) - (y))}{3 y (y - x)}$

Step 2.2.3

Factor $- 1$ out of $- 1 (- x) - (y)$ .

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

Step 2.2.4

Reorder terms.

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

Step 2.2.5

Cancel the common factor.

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

Step 2.2.6

Rewrite the expression.

$\frac{x \cdot (- 1)}{3 y}$

$\frac{x \cdot (- 1)}{3 y}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{3 y}$

Step 2.3.2

Move the negative in front of the fraction.

$- \frac{x}{3 y}$

$- \frac{x}{3 y}$

$- \frac{x}{3 y}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$