Precalculus Examples

$\frac{7 - \sqrt{- 49}}{7 + \sqrt{- 49}}$

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

Rewrite $- 49$ as $- 1 (49)$ .

$\frac{7 - \sqrt{- 1 (49)}}{7 + \sqrt{- 49}}$

Step 1.2

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$\frac{7 - (\sqrt{- 1} \cdot \sqrt{49})}{7 + \sqrt{- 49}}$

Step 1.3

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

$\frac{7 - (i \cdot \sqrt{49})}{7 + \sqrt{- 49}}$

Step 1.4

Rewrite $- 49$ as $- 1 (49)$ .

$\frac{7 - (i \cdot \sqrt{49})}{7 + \sqrt{- 1 (49)}}$

Step 1.5

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$\frac{7 - (i \cdot \sqrt{49})}{7 + \sqrt{- 1} \cdot \sqrt{49}}$

Step 1.6

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

$\frac{7 - (i \cdot \sqrt{49})}{7 + i \cdot \sqrt{49}}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $49$ as $7^{2}$ .

$\frac{7 - i \cdot \sqrt{7^{2}}}{7 + i \cdot \sqrt{49}}$

Step 2.2

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

$\frac{7 - i \cdot 7}{7 + i \cdot \sqrt{49}}$

Step 2.3

Multiply $7$ by $- 1$ .

$\frac{7 - 7 i}{7 + i \cdot \sqrt{49}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $49$ as $7^{2}$ .

$\frac{7 - 7 i}{7 + i \cdot \sqrt{7^{2}}}$

Step 3.2

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

$\frac{7 - 7 i}{7 + i \cdot 7}$

Step 3.3

Move $7$ to the left of $i$ .

$\frac{7 - 7 i}{7 + 7 i}$

Step 4

Cancel the common factor of $7 - 7 i$ and $7 + 7 i$ .

Tap for more steps...

Step 4.1

Factor $7$ out of $7$ .

$\frac{7 \cdot 1 - 7 i}{7 + 7 i}$

Step 4.2

Factor $7$ out of $- 7 i$ .

$\frac{7 \cdot 1 + 7 (- i)}{7 + 7 i}$

Step 4.3

Factor $7$ out of $7 (1) + 7 (- i)$ .

$\frac{7 (1 - i)}{7 + 7 i}$

Step 4.4

Cancel the common factors.

Tap for more steps...

Step 4.4.1

Factor $7$ out of $7$ .

$\frac{7 (1 - i)}{7 (1) + 7 i}$

Step 4.4.2

Factor $7$ out of $7 i$ .

$\frac{7 (1 - i)}{7 (1) + 7 (i)}$

Step 4.4.3

Factor $7$ out of $7 (1) + 7 (i)$ .

$\frac{7 (1 - i)}{7 (1 + i)}$

Step 4.4.4

Cancel the common factor.

$\frac{7 (1 - i)}{7 (1 + i)}$

Step 4.4.5

Rewrite the expression.

$\frac{1 - i}{1 + i}$