Simplify 17/(4-i)

$\frac{17}{4 - i}$

Step 1

Multiply the numerator and denominator of $\frac{17}{4 - i}$ by the conjugate of $4 - i$ to make the denominator real.

$\frac{17}{4 - i} \cdot \frac{4 + i}{4 + i}$

Step 2

Multiply.

Combine.

$\frac{17 (4 + i)}{(4 - i) (4 + i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{17 \cdot 4 + 17 i}{(4 - i) (4 + i)}$

Multiply $17$ by $4$ .

$\frac{68 + 17 i}{(4 - i) (4 + i)}$

Simplify the denominator.

Expand $(4 - i) (4 + i)$ using the FOIL Method.

Apply the distributive property.

$\frac{68 + 17 i}{4 (4 + i) - i (4 + i)}$

Apply the distributive property.

$\frac{68 + 17 i}{4 \cdot 4 + 4 i - i (4 + i)}$

Apply the distributive property.

$\frac{68 + 17 i}{4 \cdot 4 + 4 i - i \cdot 4 - i i}$

Simplify.

Multiply $4$ by $4$ .

$\frac{68 + 17 i}{16 + 4 i - i \cdot 4 - i i}$

Multiply $4$ by $- 1$ .

$\frac{68 + 17 i}{16 + 4 i - 4 i - i i}$

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

$\frac{68 + 17 i}{16 + 4 i - 4 i - (i^{1} i)}$

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

$\frac{68 + 17 i}{16 + 4 i - 4 i - (i^{1} i^{1})}$

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

$\frac{68 + 17 i}{16 + 4 i - 4 i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{68 + 17 i}{16 + 4 i - 4 i - i^{2}}$

Subtract $4 i$ from $4 i$ .

$\frac{68 + 17 i}{16 + 0 - i^{2}}$

Add $16$ and $0$ .

$\frac{68 + 17 i}{16 - i^{2}}$

Simplify each term.

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

$\frac{68 + 17 i}{16 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{68 + 17 i}{16 + 1}$

Add $16$ and $1$ .

$\frac{68 + 17 i}{17}$

Step 3

Cancel the common factor of $68 + 17 i$ and $17$ .

Factor $17$ out of $68$ .

$\frac{17 \cdot 4 + 17 i}{17}$

Factor $17$ out of $17 i$ .

$\frac{17 \cdot 4 + 17 (i)}{17}$

Factor $17$ out of $17 (4) + 17 (i)$ .

$\frac{17 (4 + i)}{17}$

Cancel the common factors.

Factor $17$ out of $17$ .

$\frac{17 (4 + i)}{17 (1)}$

Cancel the common factor.

$\frac{17 (4 + i)}{17 \cdot 1}$

Rewrite the expression.

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

Divide $4 + i$ by $1$ .

$4 + i$

Simplify 17/(4-i)

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