Find Where Undefined/Discontinuous 3/x+3=2/(5x)+31/10

$\frac{3}{x} + 3 = \frac{2}{5 x} + \frac{31}{10}$

Step 1

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

Subtract $\frac{2}{5 x}$ from both sides of the equation.

$\frac{3}{x} + 3 - \frac{2}{5 x} = \frac{31}{10}$

Subtract $\frac{31}{10}$ from both sides of the equation.

$\frac{3}{x} + 3 - \frac{2}{5 x} - \frac{31}{10} = 0$

Step 2

Simplify $\frac{3}{x} + 3 - \frac{2}{5 x} - \frac{31}{10}$ .

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3}{x} \cdot \frac{5}{5} - \frac{2}{5 x} + 3 - \frac{31}{10} = 0$

Write each expression with a common denominator of $x \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{x}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 5}{x \cdot 5} - \frac{2}{5 x} + 3 - \frac{31}{10} = 0$

Move $5$ to the left of $x$ .

$\frac{3 \cdot 5}{5 x} - \frac{2}{5 x} + 3 - \frac{31}{10} = 0$

Combine the numerators over the common denominator.

$\frac{3 \cdot 5 - 2}{5 x} + 3 - \frac{31}{10} = 0$

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{15 - 2}{5 x} + 3 - \frac{31}{10} = 0$

Subtract $2$ from $15$ .

$\frac{13}{5 x} + 3 - \frac{31}{10} = 0$

To write $3$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{13}{5 x} + 3 \cdot \frac{10}{10} - \frac{31}{10} = 0$

Combine $3$ and $\frac{10}{10}$ .

$\frac{13}{5 x} + \frac{3 \cdot 10}{10} - \frac{31}{10} = 0$

Combine the numerators over the common denominator.

$\frac{13}{5 x} + \frac{3 \cdot 10 - 31}{10} = 0$

Simplify the numerator.

Multiply $3$ by $10$ .

$\frac{13}{5 x} + \frac{30 - 31}{10} = 0$

Subtract $31$ from $30$ .

$\frac{13}{5 x} + \frac{- 1}{10} = 0$

Move the negative in front of the fraction.

$\frac{13}{5 x} - \frac{1}{10} = 0$

Step 3

Set the denominator in $\frac{13}{5 x}$ equal to $0$ to find where the expression is undefined.

$5 x = 0$

Step 4

Divide each term in $5 x = 0$ by $5$ and simplify.

Divide each term in $5 x = 0$ by $5$ .

$\frac{5 x}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

Divide $x$ by $1$ .

$x = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x = 0$

Step 5

Find Where Undefined/Discontinuous 3/x+3=2/(5x)+31/10

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