Precalculus Examples

$\frac{x^{2} + 9 y^{2}}{x - 3 y} + \frac{6 x y}{3 y - x}$

Step 1

Set the denominator in $\frac{x^{2} + 9 y^{2}}{x - 3 y}$ equal to $0$ to find where the expression is undefined.

$x - 3 y = 0$

Step 2

Add $3 y$ to both sides of the equation.

$x = 3 y$

Step 3

Set the denominator in $\frac{6 x y}{3 y - x}$ equal to $0$ to find where the expression is undefined.

$3 y - x = 0$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Subtract $3 y$ from both sides of the equation.

$- x = - 3 y$

Step 4.2

Divide each term in $- x = - 3 y$ by $- 1$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $- x = - 3 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3 y}{- 1}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3 y}{- 1}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 3 y}{- 1}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Move the negative one from the denominator of $\frac{- 3 y}{- 1}$ .

$x = - 1 \cdot (- 3 y)$

Step 4.2.3.2

Rewrite $- 1 \cdot (- 3 y)$ as $- (- 3 y)$ .

$x = - (- 3 y)$

Step 4.2.3.3

Multiply $- 3$ by $- 1$ .

$x = 3 y$

Step 5

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$