Precalculus Examples

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

Step 1

Set the denominator in $\frac{x^{2} - 3 x y}{(x + y) (x - y)}$ equal to $0$ to find where the expression is undefined.

$(x + y) (x - y) = 0$

Step 2

Solve for $x$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + y = 0$

$x - y = 0$

Step 2.2

Set $x + y$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x + y$ equal to $0$ .

$x + y = 0$

Step 2.2.2

Subtract $y$ from both sides of the equation.

$x = - y$

Step 2.3

Set $x - y$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x - y$ equal to $0$ .

$x - y = 0$

Step 2.3.2

Add $y$ to both sides of the equation.

$x = y$

Step 2.4

The final solution is all the values that make $(x + y) (x - y) = 0$ true.

$x = - y$

$x = y$

$x = - y$

$x = y$

Step 3

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

$x - y = 0$

Step 4

Add $y$ to both sides of the equation.

$x = y$

Step 5

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$