Find the Domain (5x+4)/(2x-5)

$\frac{5 x + 4}{2 x - 5}$

Step 1

Set the denominator in $\frac{5 x + 4}{2 x - 5}$ equal to $0$ to find where the expression is undefined.

$2 x - 5 = 0$

Step 2

Solve for $x$ .

Add $5$ to both sides of the equation.

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Step 3

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

Interval Notation:

$(- \infty, \frac{5}{2}) \cup (\frac{5}{2}, \infty)$

Set-Builder Notation:

${x | x \neq \frac{5}{2}}$

Step 4