Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- - x$ .

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

$\frac{x - y - y + 1 x}{x + y}$

Step 2.2.2

Multiply $x$ by $1$ .

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

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

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

Step 3

Simplify terms.

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Step 3.1

Add $x$ and $x$ .

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

Step 3.2

Subtract $y$ from $- y$ .

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

Step 3.3

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

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Step 3.3.1

Factor $2$ out of $2 x$ .

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

Step 3.3.2

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

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

Step 3.3.3

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

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

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

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

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