Multiply the numerator and denominator of by the conjugate of to make the denominator real.

Combine.

Simplify the numerator.

Apply the distributive property.

Multiply by .

Multiply by .

Simplify the denominator.

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Add and .

Add and .

Simplify each term.

Rewrite as .

Multiply by .

Add and .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Split the fraction into two fractions.

Move the negative in front of the fraction.

Simplify 4/(5+i)