Rewrite in Standard Form 8+i/(8-i)

$8 + \frac{i}{8 - i}$

Simplify each term.

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Multiply the numerator and denominator of $\frac{i}{8 - i}$ by the conjugate of $8 - i$ to make the denominator real.

$8 + \frac{i}{8 - i} \cdot \frac{8 + i}{8 + i}$

Multiply.

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Combine.

$8 + \frac{i (8 + i)}{(8 - i) (8 + i)}$

Simplify the numerator.

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Apply the distributive property.

$8 + \frac{i \cdot 8 + i i}{(8 - i) (8 + i)}$

Move $8$ to the left of $i$ .

$8 + \frac{8 \cdot i + i i}{(8 - i) (8 + i)}$

Multiply $i i$ .

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Raise $i$ to the power of $1$ .

$8 + \frac{8 \cdot i + i^{1} i}{(8 - i) (8 + i)}$

Raise $i$ to the power of $1$ .

$8 + \frac{8 \cdot i + i^{1} i^{1}}{(8 - i) (8 + i)}$

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

$8 + \frac{8 \cdot i + i^{1 + 1}}{(8 - i) (8 + i)}$

Add $1$ and $1$ .

$8 + \frac{8 \cdot i + i^{2}}{(8 - i) (8 + i)}$

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

$8 + \frac{8 i - 1}{(8 - i) (8 + i)}$

Reorder $8 i$ and $- 1$ .

$8 + \frac{- 1 + 8 i}{(8 - i) (8 + i)}$

Simplify the denominator.

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Expand $(8 - i) (8 + i)$ using the FOIL Method.

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Apply the distributive property.

$8 + \frac{- 1 + 8 i}{8 (8 + i) - i (8 + i)}$

Apply the distributive property.

$8 + \frac{- 1 + 8 i}{8 \cdot 8 + 8 i - i (8 + i)}$

Apply the distributive property.

$8 + \frac{- 1 + 8 i}{8 \cdot 8 + 8 i - i \cdot 8 - i i}$

Simplify.

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Multiply $8$ by $8$ .

$8 + \frac{- 1 + 8 i}{64 + 8 i - i \cdot 8 - i i}$

Multiply $8$ by $- 1$ .

$8 + \frac{- 1 + 8 i}{64 + 8 i - 8 i - i i}$

Raise $i$ to the power of $1$ .

$8 + \frac{- 1 + 8 i}{64 + 8 i - 8 i - (i^{1} i)}$

Raise $i$ to the power of $1$ .

$8 + \frac{- 1 + 8 i}{64 + 8 i - 8 i - (i^{1} i^{1})}$

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

$8 + \frac{- 1 + 8 i}{64 + 8 i - 8 i - i^{1 + 1}}$

Add $1$ and $1$ .

$8 + \frac{- 1 + 8 i}{64 + 8 i - 8 i - i^{2}}$

Subtract $8 i$ from $8 i$ .

$8 + \frac{- 1 + 8 i}{64 + 0 - i^{2}}$

Add $64$ and $0$ .

$8 + \frac{- 1 + 8 i}{64 - i^{2}}$

Simplify each term.

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

$8 + \frac{- 1 + 8 i}{64 - - 1}$

Multiply $- 1$ by $- 1$ .

$8 + \frac{- 1 + 8 i}{64 + 1}$

Add $64$ and $1$ .

$8 + \frac{- 1 + 8 i}{65}$

Split the fraction $\frac{- 1 + 8 i}{65}$ into two fractions.

$8 + \frac{- 1}{65} + \frac{8 i}{65}$

Move the negative in front of the fraction.

$8 - \frac{1}{65} + \frac{8 i}{65}$

To write $8$ as a fraction with a common denominator, multiply by $\frac{65}{65}$ .

$8 \cdot \frac{65}{65} - \frac{1}{65} + \frac{8 i}{65}$

Combine $8$ and $\frac{65}{65}$ .

$\frac{8 \cdot 65}{65} - \frac{1}{65} + \frac{8 i}{65}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 65 - 1}{65} + \frac{8 i}{65}$

Simplify the numerator.

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Multiply $8$ by $65$ .

$\frac{520 - 1}{65} + \frac{8 i}{65}$

Subtract $1$ from $520$ .

$\frac{519}{65} + \frac{8 i}{65}$

Rewrite in Standard Form 8+i/(8-i)

Solving MATH problems