Find Where Undefined/Discontinuous ( square root of 30(x-1))÷( square root of 5x^2)

$\sqrt{30 (x - 1)} \div \sqrt{5 x^{2}}$

Set the denominator in $\frac{\sqrt{30 (x - 1)}}{\sqrt{5 x^{2}}}$ equal to $0$ to find where the expression is undefined.

$\sqrt{5 x^{2}} = 0$

Solve for $x$ .

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To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{5 x^{2}}}^{2} = 0^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(5 x^{2})}^{\frac{1}{2}})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(5 x^{2})}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(5 x^{2})}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

${(5 x^{2})}^{1} = 0^{2}$

Simplify.

$5 x^{2} = 0^{2}$

Raising $0$ to any positive power yields $0$ .

$5 x^{2} = 0$

Solve for $x$ .

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Divide each term by $5$ and simplify.

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Divide each term in $5 x^{2} = 0$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{0}{5}$

Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{0}{5}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{5}$

Divide $0$ by $5$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

$\pm 0$ is equal to $0$ .

$x = 0$

Verify each of the solutions by substituting them into $\sqrt{5 x^{2}} = 0$ and solving.

$x = 0$

Set the radicand in $\sqrt{30 (x - 1)}$ less than $0$ to find where the expression is undefined.

$30 (x - 1) < 0$

Solve for $x$ .

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Divide each term by $30$ and simplify.

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Divide each term in $30 (x - 1) < 0$ by $30$ .

$\frac{30 (x - 1)}{30} < \frac{0}{30}$

Cancel the common factor of $30$ .

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Cancel the common factor.

$\frac{30 (x - 1)}{30} < \frac{0}{30}$

Divide $x - 1$ by $1$ .

$x - 1 < \frac{0}{30}$

Divide $0$ by $30$ .

$x - 1 < 0$

Add $1$ to both sides of the inequality.

$x < 1$

Set the radicand in $\sqrt{5 x^{2}}$ less than $0$ to find where the expression is undefined.

$5 x^{2} < 0$

Solve for $x$ .

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Divide each term by $5$ and simplify.

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Divide each term in $5 x^{2} < 0$ by $5$ .

$\frac{5 x^{2}}{5} < \frac{0}{5}$

Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 x^{2}}{5} < \frac{0}{5}$

Divide $x^{2}$ by $1$ .

$x^{2} < \frac{0}{5}$

Divide $0$ by $5$ .

$x^{2} < 0$

Take the square root of both sides of the inequality to eliminate the exponent on the left side.

$x < \pm \sqrt{0}$

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite $0$ as $0^{2}$ .

$x < \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x < \pm 0$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$x < 0$

Next, use the negative value of the $\pm$ to find the second solution. Since this is an inequality, flip the direction of the inequality sign on the $-$ portion of the solution.

$x > 0$

The complete solution is the result of both the positive and negative portions of the solution.

$x < 0$ and $x > 0$

This inequality has no solution.

No solution

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 $0$ .

Inequality Form:

$x < 1$

Interval Notation:

$(- \infty, 1)$

Find Where Undefined/Discontinuous ( square root of 30(x-1))÷( square root of 5x^2)

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