Finite Math Examples

Simplify ( square root of (y+2)/(y-2)+ square root of (y-2)/(y+2))/( square root of (y+2)/(y-2)- square root of (y-2)/(y+2))
Step 1
Simplify the numerator.
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Step 1.1
Rewrite as .
Step 1.2
Multiply by .
Step 1.3
Combine and simplify the denominator.
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Step 1.3.1
Multiply by .
Step 1.3.2
Raise to the power of .
Step 1.3.3
Raise to the power of .
Step 1.3.4
Use the power rule to combine exponents.
Step 1.3.5
Add and .
Step 1.3.6
Rewrite as .
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Step 1.3.6.1
Use to rewrite as .
Step 1.3.6.2
Apply the power rule and multiply exponents, .
Step 1.3.6.3
Combine and .
Step 1.3.6.4
Cancel the common factor of .
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Step 1.3.6.4.1
Cancel the common factor.
Step 1.3.6.4.2
Rewrite the expression.
Step 1.3.6.5
Simplify.
Step 1.4
Combine using the product rule for radicals.
Step 1.5
Rewrite as .
Step 1.6
Multiply by .
Step 1.7
Combine and simplify the denominator.
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Step 1.7.1
Multiply by .
Step 1.7.2
Raise to the power of .
Step 1.7.3
Raise to the power of .
Step 1.7.4
Use the power rule to combine exponents.
Step 1.7.5
Add and .
Step 1.7.6
Rewrite as .
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Step 1.7.6.1
Use to rewrite as .
Step 1.7.6.2
Apply the power rule and multiply exponents, .
Step 1.7.6.3
Combine and .
Step 1.7.6.4
Cancel the common factor of .
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Step 1.7.6.4.1
Cancel the common factor.
Step 1.7.6.4.2
Rewrite the expression.
Step 1.7.6.5
Simplify.
Step 1.8
Combine using the product rule for radicals.
Step 1.9
To write as a fraction with a common denominator, multiply by .
Step 1.10
To write as a fraction with a common denominator, multiply by .
Step 1.11
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.11.1
Multiply by .
Step 1.11.2
Multiply by .
Step 1.11.3
Reorder the factors of .
Step 1.12
Combine the numerators over the common denominator.
Step 1.13
Rewrite in a factored form.
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Step 1.13.1
Use to rewrite as .
Step 1.13.2
Use to rewrite as .
Step 1.13.3
Expand using the FOIL Method.
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Step 1.13.3.1
Apply the distributive property.
Step 1.13.3.2
Apply the distributive property.
Step 1.13.3.3
Apply the distributive property.
Step 1.13.4
Combine the opposite terms in .
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Step 1.13.4.1
Reorder the factors in the terms and .
Step 1.13.4.2
Add and .
Step 1.13.4.3
Add and .
Step 1.13.5
Simplify each term.
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Step 1.13.5.1
Multiply by .
Step 1.13.5.2
Multiply by .
Step 1.13.6
Apply the distributive property.
Step 1.13.7
Move to the left of .
Step 1.13.8
Expand using the FOIL Method.
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Step 1.13.8.1
Apply the distributive property.
Step 1.13.8.2
Apply the distributive property.
Step 1.13.8.3
Apply the distributive property.
Step 1.13.9
Combine the opposite terms in .
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Step 1.13.9.1
Reorder the factors in the terms and .
Step 1.13.9.2
Subtract from .
Step 1.13.9.3
Add and .
Step 1.13.10
Simplify each term.
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Step 1.13.10.1
Multiply by .
Step 1.13.10.2
Multiply by .
Step 1.13.11
Apply the distributive property.
Step 1.13.12
Move to the left of .
Step 1.13.13
Add and .
Step 1.13.14
Subtract from .
Step 1.13.15
Add and .
Step 1.13.16
Reorder the factors of .
Step 2
Simplify the denominator.
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Step 2.1
Rewrite as .
Step 2.2
Multiply by .
Step 2.3
Combine and simplify the denominator.
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Step 2.3.1
Multiply by .
Step 2.3.2
Raise to the power of .
Step 2.3.3
Raise to the power of .
Step 2.3.4
Use the power rule to combine exponents.
Step 2.3.5
Add and .
Step 2.3.6
Rewrite as .
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Step 2.3.6.1
Use to rewrite as .
Step 2.3.6.2
Apply the power rule and multiply exponents, .
Step 2.3.6.3
Combine and .
Step 2.3.6.4
Cancel the common factor of .
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Step 2.3.6.4.1
Cancel the common factor.
Step 2.3.6.4.2
Rewrite the expression.
Step 2.3.6.5
Simplify.
Step 2.4
Combine using the product rule for radicals.
Step 2.5
Rewrite as .
Step 2.6
Multiply by .
Step 2.7
Combine and simplify the denominator.
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Step 2.7.1
Multiply by .
Step 2.7.2
Raise to the power of .
Step 2.7.3
Raise to the power of .
Step 2.7.4
Use the power rule to combine exponents.
Step 2.7.5
Add and .
Step 2.7.6
Rewrite as .
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Step 2.7.6.1
Use to rewrite as .
Step 2.7.6.2
Apply the power rule and multiply exponents, .
Step 2.7.6.3
Combine and .
Step 2.7.6.4
Cancel the common factor of .
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Step 2.7.6.4.1
Cancel the common factor.
Step 2.7.6.4.2
Rewrite the expression.
Step 2.7.6.5
Simplify.
Step 2.8
Combine using the product rule for radicals.
Step 2.9
To write as a fraction with a common denominator, multiply by .
Step 2.10
To write as a fraction with a common denominator, multiply by .
Step 2.11
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.11.1
Multiply by .
Step 2.11.2
Multiply by .
Step 2.11.3
Reorder the factors of .
Step 2.12
Combine the numerators over the common denominator.
Step 2.13
Rewrite in a factored form.
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Step 2.13.1
Use to rewrite as .
Step 2.13.2
Use to rewrite as .
Step 2.13.3
Expand using the FOIL Method.
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Step 2.13.3.1
Apply the distributive property.
Step 2.13.3.2
Apply the distributive property.
Step 2.13.3.3
Apply the distributive property.
Step 2.13.4
Combine the opposite terms in .
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Step 2.13.4.1
Reorder the factors in the terms and .
Step 2.13.4.2
Add and .
Step 2.13.4.3
Add and .
Step 2.13.5
Simplify each term.
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Step 2.13.5.1
Multiply by .
Step 2.13.5.2
Multiply by .
Step 2.13.6
Apply the distributive property.
Step 2.13.7
Move to the left of .
Step 2.13.8
Expand using the FOIL Method.
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Step 2.13.8.1
Apply the distributive property.
Step 2.13.8.2
Apply the distributive property.
Step 2.13.8.3
Apply the distributive property.
Step 2.13.9
Combine the opposite terms in .
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Step 2.13.9.1
Reorder the factors in the terms and .
Step 2.13.9.2
Subtract from .
Step 2.13.9.3
Add and .
Step 2.13.10
Simplify each term.
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Step 2.13.10.1
Multiply by .
Step 2.13.10.2
Multiply by .
Step 2.13.11
Apply the distributive property.
Step 2.13.12
Multiply by .
Step 2.13.13
Subtract from .
Step 2.13.14
Add and .
Step 2.13.15
Add and .
Step 3
Multiply the numerator by the reciprocal of the denominator.
Step 4
Combine.
Step 5
Factor out of .
Step 6
Cancel the common factors.
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Step 6.1
Factor out of .
Step 6.2
Cancel the common factor.
Step 6.3
Rewrite the expression.
Step 7
Cancel the common factor.
Step 8
Rewrite the expression.
Step 9
Cancel the common factor of .
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Step 9.1
Cancel the common factor.
Step 9.2
Rewrite the expression.
Step 10
Cancel the common factor of .
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Step 10.1
Cancel the common factor.
Step 10.2
Rewrite the expression.