Precalculus Examples

$f (x, y) = \frac{x^{4} + y^{4}}{x y}$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{x^{4} + y^{4}}{x y} = f (x, y)$

Step 2

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 2.1

Subtract $f (x, y)$ from both sides of the equation.

$\frac{x^{4} + y^{4}}{x y} - f (x, y) = 0$

Step 2.2

To write $- f (x, y)$ as a fraction with a common denominator, multiply by $\frac{x y}{x y}$ .

$\frac{x^{4} + y^{4}}{x y} - f (x, y) \cdot \frac{x y}{x y} = 0$

Step 2.3

Combine $- f (x, y)$ and $\frac{x y}{x y}$ .

$\frac{x^{4} + y^{4}}{x y} + \frac{- f (x, y) (x y)}{x y} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x^{4} + y^{4} - f (x, y) (x y)}{x y} = 0$

Step 2.5

Reorder factors in $\frac{x^{4} + y^{4} - f (x, y) (x y)}{x y}$ .

$\frac{x^{4} + y^{4} - x y f (x, y)}{x y} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4