Find the Domain 7y-xy=3

$7 y - x y = 3$

Step 1

Factor $y$ out of $7 y - x y$ .

Factor $y$ out of $7 y$ .

$y \cdot 7 - x y = 3$

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

$y \cdot 7 + y (- x) = 3$

Factor $y$ out of $y \cdot 7 + y (- x)$ .

$y (7 - x) = 3$

Step 2

Divide each term in $y (7 - x) = 3$ by $7 - x$ and simplify.

Divide each term in $y (7 - x) = 3$ by $7 - x$ .

$\frac{y (7 - x)}{7 - x} = \frac{3}{7 - x}$

Simplify the left side.

Cancel the common factor of $7 - x$ .

Cancel the common factor.

$\frac{y (7 - x)}{7 - x} = \frac{3}{7 - x}$

Divide $y$ by $1$ .

$y = \frac{3}{7 - x}$

Step 3

Set the denominator in $\frac{3}{7 - x}$ equal to $0$ to find where the expression is undefined.

$7 - x = 0$

Step 4

Solve for $x$ .

Subtract $7$ from both sides of the equation.

$- x = - 7$

Divide each term in $- x = - 7$ by $- 1$ and simplify.

Divide each term in $- x = - 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 7}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$x = 7$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 7) \cup (7, \infty)$

Set-Builder Notation:

${x | x \neq 7}$

Step 6