Find Where Undefined/Discontinuous 3/x+3=4/(5x)+31/10

$\frac{3}{x} + 3 = \frac{4}{5 x} + \frac{31}{10}$

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

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Move $\frac{4}{5 x}$ to the left side of the equation by subtracting it from both sides.

$\frac{3}{x} + 3 - \frac{4}{5 x} = \frac{31}{10}$

Move $\frac{31}{10}$ to the left side of the equation by subtracting it from both sides.

$\frac{3}{x} + 3 - \frac{4}{5 x} - \frac{31}{10} = 0$

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

$x = 0$

Set the denominator in $\frac{4}{5 x}$ equal to $0$ to find where the expression is undefined.

$5 x = 0$

Divide each term by $5$ and simplify.

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

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

Cancel the common factor of $5$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $0$ by $5$ .

$x = 0$

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = 0$

Find Where Undefined/Discontinuous 3/x+3=4/(5x)+31/10

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