Calculus Examples

$f (x) = \frac{7 + x}{x (x - 6)}$

Step 1

Set the denominator in $\frac{7 + x}{x (x - 6)}$ equal to $0$ to find where the expression is undefined.

$x (x - 6) = 0$

Step 2

Solve for $x$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 6 = 0$

Step 2.2

Set $x$ equal to $0$ .

$x = 0$

Step 2.3

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 2.3.2

Add $6$ to both sides of the equation.

$x = 6$

Step 2.4

The final solution is all the values that make $x (x - 6) = 0$ true.

$x = 0, 6$

Step 3

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 $0$ .

$x = 0, x = 6$

Step 4