Finite Math Examples

$f (x) = \frac{\sqrt{x}}{x - \sqrt{x}}$

Step 1

Set $\frac{\sqrt{x}}{x - \sqrt{x}}$ equal to $0$ .

$\frac{\sqrt{x}}{x - \sqrt{x}} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$\sqrt{x} = 0$

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

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

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

Step 2.2.2

Simplify each side of the equation.

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Step 2.2.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

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

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

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Step 2.2.2.2.1.1

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

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Step 2.2.2.2.1.1.1

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

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

Step 2.2.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.2.2.1.1.2.2

Rewrite the expression.

$x^{1} = 0^{2}$

Step 2.2.2.2.1.2

Simplify.

$x = 0^{2}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

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

$x = 0$

Step 2.3

Exclude the solutions that do not make $\frac{\sqrt{x}}{x - \sqrt{x}} = 0$ true.

$No solution$