Find the Domain ((x-7)/(x+4))÷(x/(x+3))

$\frac{x - 7}{x + 4} \div \frac{x}{x + 3}$

Step 1

Set the denominator in $\frac{x - 7}{x + 4}$ equal to $0$ to find where the expression is undefined.

$x + 4 = 0$

Step 2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 3

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

$x + 3 = 0$

Step 4

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 5

Set the denominator in $\frac{\frac{x - 7}{x + 4}}{\frac{x}{x + 3}}$ equal to $0$ to find where the expression is undefined.

$\frac{x}{x + 3} = 0$

Step 6

Set the numerator equal to zero.

$x = 0$

Step 7

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

Interval Notation:

$(- \infty, - 4) \cup (- 4, - 3) \cup (- 3, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 3, - 4}$

Step 8