Precalculus Examples

Write in Standard Form 2/(1+i)-3/(1-i)
Step 1
Simplify each term.
Tap for more steps...
Step 1.1
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 1.2
Multiply.
Tap for more steps...
Step 1.2.1
Combine.
Step 1.2.2
Simplify the numerator.
Tap for more steps...
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.
Tap for more steps...
Step 1.2.3.1
Expand using the FOIL Method.
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
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 .
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
Step 1.5.1
Combine.
Step 1.5.2
Simplify the numerator.
Tap for more steps...
Step 1.5.2.1
Apply the distributive property.
Step 1.5.2.2
Multiply by .
Step 1.5.3
Simplify the denominator.
Tap for more steps...
Step 1.5.3.1
Expand using the FOIL Method.
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
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
Write as a fraction with a common denominator.
Step 3
Combine the numerators over the common denominator.
Step 4
Subtract from .
Step 5
Move the negative in front of the fraction.
Step 6
To write as a fraction with a common denominator, multiply by .
Step 7
Combine and .
Step 8
Combine the numerators over the common denominator.
Step 9
Move the negative in front of the fraction.