Precalculus Examples

$y \sqrt{x} = 2$

Step 1

Divide each term in $y \sqrt{x} = 2$ by $\sqrt{x}$ .

$\frac{y \sqrt{x}}{\sqrt{x}} = \frac{2}{\sqrt{x}}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\sqrt{x}$ .

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Step 2.1.1

Cancel the common factor.

$\frac{y \sqrt{x}}{\sqrt{x}} = \frac{2}{\sqrt{x}}$

Step 2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{\sqrt{x}}$

Step 3

Simplify the right side.

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Step 3.1

Multiply $\frac{2}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$y = \frac{2}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Step 3.2

Combine and simplify the denominator.

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Step 3.2.1

Multiply $\frac{2}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$y = \frac{2 \sqrt{x}}{\sqrt{x} \sqrt{x}}$

Step 3.2.2

Raise $\sqrt{x}$ to the power of $1$ .

$y = \frac{2 \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}}$

Step 3.2.3

Raise $\sqrt{x}$ to the power of $1$ .

$y = \frac{2 \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}}$

Step 3.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{2 \sqrt{x}}{{\sqrt{x}}^{1 + 1}}$

Step 3.2.5

Add $1$ and $1$ .

$y = \frac{2 \sqrt{x}}{{\sqrt{x}}^{2}}$

Step 3.2.6

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 3.2.6.1

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

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

Step 3.2.6.2

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

$y = \frac{2 \sqrt{x}}{x^{\frac{1}{2} \cdot 2}}$

Step 3.2.6.3

Combine $\frac{1}{2}$ and $2$ .

$y = \frac{2 \sqrt{x}}{x^{\frac{2}{2}}}$

Step 3.2.6.4

Cancel the common factor of $2$ .

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Step 3.2.6.4.1

Cancel the common factor.

$y = \frac{2 \sqrt{x}}{x^{\frac{2}{2}}}$

Step 3.2.6.4.2

Rewrite the expression.

$y = \frac{2 \sqrt{x}}{x^{1}}$

Step 3.2.6.5

Simplify.

$y = \frac{2 \sqrt{x}}{x}$