Precalculus Examples

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

Step 1

Set the denominator in $\frac{2 (x - y)}{y (x + y)}$ equal to $0$ to find where the expression is undefined.

$y (x + y) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $y (x + y) = 0$ by $y$ and simplify.

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Step 2.1.1

Divide each term in $y (x + y) = 0$ by $y$ .

$\frac{y (x + y)}{y} = \frac{0}{y}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $y$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{y (x + y)}{y} = \frac{0}{y}$

Step 2.1.2.1.2

Divide $x + y$ by $1$ .

$x + y = \frac{0}{y}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $y$ .

$x + y = 0$

Step 2.2

Subtract $y$ from both sides of the equation.

$x = - y$

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$