Find Where Undefined/Discontinuous 4/x=1/(4x)+3

$\frac{4}{x} = \frac{1}{4 x} + 3$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{1}{4 x}$ from both sides of the equation.

$\frac{4}{x} - \frac{1}{4 x} = 3$

Subtract $3$ from both sides of the equation.

$\frac{4}{x} - \frac{1}{4 x} - 3 = 0$

Step 2

Simplify $\frac{4}{x} - \frac{1}{4 x} - 3$ .

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

$\frac{4}{x} \cdot \frac{4}{4} - \frac{1}{4 x} - 3 = 0$

Write each expression with a common denominator of $x \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x}$ by $\frac{4}{4}$ .

$\frac{4 \cdot 4}{x \cdot 4} - \frac{1}{4 x} - 3 = 0$

Move $4$ to the left of $x$ .

$\frac{4 \cdot 4}{4 x} - \frac{1}{4 x} - 3 = 0$

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 - 1}{4 x} - 3 = 0$

Simplify the numerator.

Multiply $4$ by $4$ .

$\frac{16 - 1}{4 x} - 3 = 0$

Subtract $1$ from $16$ .

$\frac{15}{4 x} - 3 = 0$

Step 3

Set the denominator in $\frac{15}{4 x}$ equal to $0$ to find where the expression is undefined.

$4 x = 0$

Step 4

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

Step 5