Basic Math Examples

Simplify ( square root of 2+1)/( square root of 3+1)-( square root of 2-1)/( square root of 5- square root of 3)
Step 1
Simplify each term.
Tap for more steps...
Step 1.1
Multiply by .
Step 1.2
Multiply by .
Step 1.3
Expand the denominator using the FOIL method.
Step 1.4
Simplify.
Step 1.5
Expand using the FOIL Method.
Tap for more steps...
Step 1.5.1
Apply the distributive property.
Step 1.5.2
Apply the distributive property.
Step 1.5.3
Apply the distributive property.
Step 1.6
Simplify each term.
Tap for more steps...
Step 1.6.1
Combine using the product rule for radicals.
Step 1.6.2
Multiply by .
Step 1.6.3
Move to the left of .
Step 1.6.4
Rewrite as .
Step 1.6.5
Multiply by .
Step 1.6.6
Multiply by .
Step 1.7
Multiply by .
Step 1.8
Multiply by .
Step 1.9
Expand the denominator using the FOIL method.
Step 1.10
Simplify.
Step 1.11
Expand using the FOIL Method.
Tap for more steps...
Step 1.11.1
Apply the distributive property.
Step 1.11.2
Apply the distributive property.
Step 1.11.3
Apply the distributive property.
Step 1.12
Simplify each term.
Tap for more steps...
Step 1.12.1
Combine using the product rule for radicals.
Step 1.12.2
Multiply by .
Step 1.12.3
Combine using the product rule for radicals.
Step 1.12.4
Multiply by .
Step 1.12.5
Rewrite as .
Step 1.12.6
Rewrite as .
Step 2
Combine the numerators over the common denominator.
Step 3
Simplify each term.
Tap for more steps...
Step 3.1
Apply the distributive property.
Step 3.2
Simplify.
Tap for more steps...
Step 3.2.1
Multiply .
Tap for more steps...
Step 3.2.1.1
Multiply by .
Step 3.2.1.2
Multiply by .
Step 3.2.2
Multiply .
Tap for more steps...
Step 3.2.2.1
Multiply by .
Step 3.2.2.2
Multiply by .
Step 4
Simplify terms.
Tap for more steps...
Step 4.1
Subtract from .
Step 4.2
Subtract from .
Step 4.3
Add and .
Step 4.4
Factor out of .
Step 4.5
Rewrite as .
Step 4.6
Factor out of .
Step 4.7
Factor out of .
Step 4.8
Factor out of .
Step 4.9
Factor out of .
Step 4.10
Factor out of .
Step 4.11
Factor out of .
Step 4.12
Factor out of .
Step 4.13
Simplify the expression.
Tap for more steps...
Step 4.13.1
Rewrite as .
Step 4.13.2
Move the negative in front of the fraction.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: