Find the Domain f(x)=(2x)/(5x-25)

$f (x) = \frac{2 x}{5 x - 25}$

Step 1

Set the denominator in $\frac{2 x}{5 x - 25}$ equal to $0$ to find where the expression is undefined.

$5 x - 25 = 0$

Step 2

Solve for $x$ .

Add $25$ to both sides of the equation.

$5 x = 25$

Divide each term in $5 x = 25$ by $5$ and simplify.

Divide each term in $5 x = 25$ by $5$ .

$\frac{5 x}{5} = \frac{25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{25}{5}$

Divide $x$ by $1$ .

$x = \frac{25}{5}$

Simplify the right side.

Divide $25$ by $5$ .

$x = 5$

Step 3

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

Interval Notation:

$(- \infty, 5) \cup (5, \infty)$

Set-Builder Notation:

${x | x \neq 5}$

Step 4