Algebra Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $x$ and $x^{3}$ .

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Step 1.1.1

Factor $x$ out of $5 x (x - y)$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

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

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

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

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

Step 1.2

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

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Step 1.2.1

Factor $- 1$ out of $x$ .

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

Step 1.2.2

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

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

Step 1.2.3

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

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

Step 1.2.4

Reorder terms.

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

Step 1.2.5

Cancel the common factor.

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

Step 1.2.6

Rewrite the expression.

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

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

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

Step 2

Multiply $5$ by $- 1$ .

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

Step 3

Move the negative in front of the fraction.

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

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