Find Where Undefined/Discontinuous 1/(x-4)+4=21/(x-4)

$\frac{1}{x - 4} + 4 = \frac{21}{x - 4}$

Step 1

Subtract $\frac{21}{x - 4}$ from both sides of the equation.

$\frac{1}{x - 4} + 4 - \frac{21}{x - 4} = 0$

Step 2

Simplify $\frac{1}{x - 4} + 4 - \frac{21}{x - 4}$ .

Combine the numerators over the common denominator.

$4 + \frac{1 - 21}{x - 4} = 0$

Subtract $21$ from $1$ .

$4 + \frac{- 20}{x - 4} = 0$

Move the negative in front of the fraction.

$4 - \frac{20}{x - 4} = 0$

To write $4$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$\frac{4 (x - 4)}{x - 4} - \frac{20}{x - 4} = 0$

Combine the numerators over the common denominator.

$\frac{4 (x - 4) - 20}{x - 4} = 0$

Simplify the numerator.

Factor $4$ out of $4 (x - 4) - 20$ .

Factor $4$ out of $- 20$ .

$\frac{4 (x - 4) + 4 \cdot - 5}{x - 4} = 0$

Factor $4$ out of $4 (x - 4) + 4 \cdot - 5$ .

$\frac{4 (x - 4 - 5)}{x - 4} = 0$

Subtract $5$ from $- 4$ .

$\frac{4 (x - 9)}{x - 4} = 0$

Step 3

Set the denominator in $\frac{4 (x - 9)}{x - 4}$ equal to $0$ to find where the expression is undefined.

$x - 4 = 0$

Step 4

Add $4$ to both sides of the equation.

$x = 4$

Step 5