Find Where Undefined/Discontinuous 3/x+4=5/(3x)+25/6

$\frac{3}{x} + 4 = \frac{5}{3 x} + \frac{25}{6}$

Step 1

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

Subtract $\frac{5}{3 x}$ from both sides of the equation.

$\frac{3}{x} + 4 - \frac{5}{3 x} = \frac{25}{6}$

Subtract $\frac{25}{6}$ from both sides of the equation.

$\frac{3}{x} + 4 - \frac{5}{3 x} - \frac{25}{6} = 0$

Step 2

Simplify $\frac{3}{x} + 4 - \frac{5}{3 x} - \frac{25}{6}$ .

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{x} \cdot \frac{3}{3} - \frac{5}{3 x} + 4 - \frac{25}{6} = 0$

Write each expression with a common denominator of $x \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{x}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{x \cdot 3} - \frac{5}{3 x} + 4 - \frac{25}{6} = 0$

Move $3$ to the left of $x$ .

$\frac{3 \cdot 3}{3 x} - \frac{5}{3 x} + 4 - \frac{25}{6} = 0$

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 - 5}{3 x} + 4 - \frac{25}{6} = 0$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 - 5}{3 x} + 4 - \frac{25}{6} = 0$

Subtract $5$ from $9$ .

$\frac{4}{3 x} + 4 - \frac{25}{6} = 0$

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{4}{3 x} + 4 \cdot \frac{6}{6} - \frac{25}{6} = 0$

Combine $4$ and $\frac{6}{6}$ .

$\frac{4}{3 x} + \frac{4 \cdot 6}{6} - \frac{25}{6} = 0$

Combine the numerators over the common denominator.

$\frac{4}{3 x} + \frac{4 \cdot 6 - 25}{6} = 0$

Simplify the numerator.

Multiply $4$ by $6$ .

$\frac{4}{3 x} + \frac{24 - 25}{6} = 0$

Subtract $25$ from $24$ .

$\frac{4}{3 x} + \frac{- 1}{6} = 0$

Move the negative in front of the fraction.

$\frac{4}{3 x} - \frac{1}{6} = 0$

Step 3

Set the denominator in $\frac{4}{3 x}$ equal to $0$ to find where the expression is undefined.

$3 x = 0$

Step 4

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$

Step 5

Find Where Undefined/Discontinuous 3/x+4=5/(3x)+25/6

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