Find Where Undefined/Discontinuous 4/x=23/(8x)+3

$\frac{4}{x} = \frac{23}{8 x} + 3$

Step 1

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

Subtract $\frac{23}{8 x}$ from both sides of the equation.

$\frac{4}{x} - \frac{23}{8 x} = 3$

Subtract $3$ from both sides of the equation.

$\frac{4}{x} - \frac{23}{8 x} - 3 = 0$

Step 2

Simplify $\frac{4}{x} - \frac{23}{8 x} - 3$ .

To write $\frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{4}{x} \cdot \frac{8}{8} - \frac{23}{8 x} - 3 = 0$

Write each expression with a common denominator of $x \cdot 8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x}$ by $\frac{8}{8}$ .

$\frac{4 \cdot 8}{x \cdot 8} - \frac{23}{8 x} - 3 = 0$

Move $8$ to the left of $x$ .

$\frac{4 \cdot 8}{8 x} - \frac{23}{8 x} - 3 = 0$

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 - 23}{8 x} - 3 = 0$

Simplify the numerator.

Multiply $4$ by $8$ .

$\frac{32 - 23}{8 x} - 3 = 0$

Subtract $23$ from $32$ .

$\frac{9}{8 x} - 3 = 0$

Step 3

Set the denominator in $\frac{9}{8 x}$ equal to $0$ to find where the expression is undefined.

$8 x = 0$

Step 4

Divide each term in $8 x = 0$ by $8$ and simplify.

Divide each term in $8 x = 0$ by $8$ .

$\frac{8 x}{8} = \frac{0}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{0}{8}$

Divide $x$ by $1$ .

$x = \frac{0}{8}$

Simplify the right side.

Divide $0$ by $8$ .

$x = 0$

Step 5