Precalculus Examples

Simplify 2/(1+i)-3/(1-i)
Step 1
Simplify each term.
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Step 1.1
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 1.2
Multiply.
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Step 1.2.1
Combine.
Step 1.2.2
Simplify the numerator.
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Step 1.2.2.1
Apply the distributive property.
Step 1.2.2.2
Multiply by .
Step 1.2.2.3
Multiply by .
Step 1.2.3
Simplify the denominator.
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Step 1.2.3.1
Expand using the FOIL Method.
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Step 1.2.3.1.1
Apply the distributive property.
Step 1.2.3.1.2
Apply the distributive property.
Step 1.2.3.1.3
Apply the distributive property.
Step 1.2.3.2
Simplify.
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Step 1.2.3.2.1
Multiply by .
Step 1.2.3.2.2
Multiply by .
Step 1.2.3.2.3
Multiply by .
Step 1.2.3.2.4
Multiply by .
Step 1.2.3.2.5
Raise to the power of .
Step 1.2.3.2.6
Raise to the power of .
Step 1.2.3.2.7
Use the power rule to combine exponents.
Step 1.2.3.2.8
Add and .
Step 1.2.3.2.9
Add and .
Step 1.2.3.2.10
Add and .
Step 1.2.3.3
Simplify each term.
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Step 1.2.3.3.1
Rewrite as .
Step 1.2.3.3.2
Multiply by .
Step 1.2.3.4
Add and .
Step 1.3
Cancel the common factor of and .
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Step 1.3.1
Factor out of .
Step 1.3.2
Factor out of .
Step 1.3.3
Factor out of .
Step 1.3.4
Cancel the common factors.
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Step 1.3.4.1
Factor out of .
Step 1.3.4.2
Cancel the common factor.
Step 1.3.4.3
Rewrite the expression.
Step 1.3.4.4
Divide by .
Step 1.4
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 1.5
Multiply.
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Step 1.5.1
Combine.
Step 1.5.2
Simplify the numerator.
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Step 1.5.2.1
Apply the distributive property.
Step 1.5.2.2
Multiply by .
Step 1.5.3
Simplify the denominator.
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Step 1.5.3.1
Expand using the FOIL Method.
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Step 1.5.3.1.1
Apply the distributive property.
Step 1.5.3.1.2
Apply the distributive property.
Step 1.5.3.1.3
Apply the distributive property.
Step 1.5.3.2
Simplify.
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Step 1.5.3.2.1
Multiply by .
Step 1.5.3.2.2
Multiply by .
Step 1.5.3.2.3
Raise to the power of .
Step 1.5.3.2.4
Raise to the power of .
Step 1.5.3.2.5
Use the power rule to combine exponents.
Step 1.5.3.2.6
Add and .
Step 1.5.3.2.7
Subtract from .
Step 1.5.3.2.8
Add and .
Step 1.5.3.3
Simplify each term.
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Step 1.5.3.3.1
Rewrite as .
Step 1.5.3.3.2
Multiply by .
Step 1.5.3.4
Add and .
Step 1.6
Split the fraction into two fractions.
Step 1.7
Apply the distributive property.
Step 2
Simplify the expression.
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Step 2.1
Write as a fraction with a common denominator.
Step 2.2
Combine the numerators over the common denominator.
Step 2.3
Subtract from .
Step 2.4
Move the negative in front of the fraction.
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Simplify the expression.
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Step 5.1
Combine the numerators over the common denominator.
Step 5.2
Move the negative in front of the fraction.