Algebra Examples

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

Step 1

Cancel the common factor of $x$ .

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Step 1.1

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

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

Step 1.2

Cancel the common factor.

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

Step 1.3

Rewrite the expression.

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

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

Step 2

Multiply $x - y$ by $\frac{2 x}{y (y - x)}$ .

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

Step 3

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

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Step 3.1

Factor $- 1$ out of $x$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Reorder terms.

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

Step 3.5

Cancel the common factor.

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

Step 3.6

Rewrite the expression.

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

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $2$ .

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

Step 4.2

Move the negative in front of the fraction.

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

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

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