Algebra Examples

$\frac{x^{2} - 25}{x} \div \frac{x + 5}{x - 5}$

Step 1

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

$x = 0$

Step 2

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

$x - 5 = 0$

Step 3

Add $5$ to both sides of the equation.

$x = 5$

Step 4

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

$\frac{x + 5}{x - 5} = 0$

Step 5

Solve for $x$ .

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Step 5.1

Set the numerator equal to zero.

$x + 5 = 0$

Step 5.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 6

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = - 5, x = 0, x = 5$

Step 7