Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $i^{2}$ as $- 1$ .

$\frac{i - 1 + i^{3}}{i^{3} + i^{4} + i^{5}}$

Step 1.2

Factor out $i^{2}$ .

$\frac{i - 1 + i^{2} \cdot i}{i^{3} + i^{4} + i^{5}}$

Step 1.3

Rewrite $i^{2}$ as $- 1$ .

$\frac{i - 1 - 1 \cdot i}{i^{3} + i^{4} + i^{5}}$

Step 1.4

Rewrite $- 1 i$ as $- i$ .

$\frac{i - 1 - i}{i^{3} + i^{4} + i^{5}}$

Step 1.5

Subtract $i$ from $i$ .

$\frac{0 - 1}{i^{3} + i^{4} + i^{5}}$

Step 1.6

Subtract $1$ from $0$ .

$\frac{- 1}{i^{3} + i^{4} + i^{5}}$

$\frac{- 1}{i^{3} + i^{4} + i^{5}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Factor out $i^{2}$ .

$\frac{- 1}{i^{2} \cdot i + i^{4} + i^{5}}$

Step 2.2

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 1}{- 1 \cdot i + i^{4} + i^{5}}$

Step 2.3

Rewrite $- 1 i$ as $- i$ .

$\frac{- 1}{- i + i^{4} + i^{5}}$

Step 2.4

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 2.4.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$\frac{- 1}{- i + {(i^{2})}^{2} + i^{5}}$

Step 2.4.2

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 1}{- i + {(- 1)}^{2} + i^{5}}$

Step 2.4.3

Raise $- 1$ to the power of $2$ .

$\frac{- 1}{- i + 1 + i^{5}}$

$\frac{- 1}{- i + 1 + i^{5}}$

Step 2.5

Factor out $i^{4}$ .

$\frac{- 1}{- i + 1 + i^{4} i}$

Step 2.6

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 2.6.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$\frac{- 1}{- i + 1 + {(i^{2})}^{2} i}$

Step 2.6.2

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 1}{- i + 1 + {(- 1)}^{2} i}$

Step 2.6.3

Raise $- 1$ to the power of $2$ .

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

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

Step 2.7

Multiply $i$ by $1$ .

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

Step 2.8

Add $- i$ and $i$ .

$\frac{- 1}{0 + 1}$

Step 2.9

Add $0$ and $1$ .

$\frac{- 1}{1}$

$\frac{- 1}{1}$

Step 3

Divide $- 1$ by $1$ .

$- 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$