Algebra Examples

$\frac{\sqrt{9} + \sqrt{4}}{\sqrt{- 9} + \sqrt{- 4}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{\sqrt{9} + \sqrt{4}}{\sqrt{- 1 (9)} + \sqrt{- 4}}$

Step 1.2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\frac{\sqrt{9} + \sqrt{4}}{\sqrt{- 1} \cdot \sqrt{9} + \sqrt{- 4}}$

Step 1.3

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{\sqrt{9} + \sqrt{4}}{i \cdot \sqrt{9} + \sqrt{- 4}}$

Step 1.4

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{\sqrt{9} + \sqrt{4}}{i \cdot \sqrt{9} + \sqrt{- 1 (4)}}$

Step 1.5

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\frac{\sqrt{9} + \sqrt{4}}{i \cdot \sqrt{9} + \sqrt{- 1} \cdot \sqrt{4}}$

Step 1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{\sqrt{9} + \sqrt{4}}{i \cdot \sqrt{9} + i \cdot \sqrt{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2}} + \sqrt{4}}{i \cdot \sqrt{9} + i \cdot \sqrt{4}}$

Step 2.2

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

$\frac{3 + \sqrt{4}}{i \cdot \sqrt{9} + i \cdot \sqrt{4}}$

Step 2.3

Rewrite $4$ as $2^{2}$ .

$\frac{3 + \sqrt{2^{2}}}{i \cdot \sqrt{9} + i \cdot \sqrt{4}}$

Step 2.4

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

$\frac{3 + 2}{i \cdot \sqrt{9} + i \cdot \sqrt{4}}$

Step 2.5

Add $3$ and $2$ .

$\frac{5}{i \cdot \sqrt{9} + i \cdot \sqrt{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Factor $i$ out of $i \cdot \sqrt{9} + i \cdot \sqrt{4}$ .

$\frac{5}{i (\sqrt{9} + \sqrt{4})}$

Step 3.2

Rewrite $9$ as $3^{2}$ .

$\frac{5}{i (\sqrt{3^{2}} + \sqrt{4})}$

Step 3.3

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

$\frac{5}{i (3 + \sqrt{4})}$

Step 3.4

Rewrite $4$ as $2^{2}$ .

$\frac{5}{i (3 + \sqrt{2^{2}})}$

Step 3.5

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

$\frac{5}{i (3 + 2)}$

Step 3.6

Add $3$ and $2$ .

$\frac{5}{i \cdot 5}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

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

$\frac{5}{5 i}$

Step 4.2

Cancel the common factor of $5$ .

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Step 4.2.1

Cancel the common factor.

$\frac{5}{5 i}$

Step 4.2.2

Rewrite the expression.

$\frac{1}{i}$