Basic Math Examples

Solve for a ( square root of 11- square root of 7)/( square root of 11+ square root of 7)=a-b square root of 77
Step 1
Rewrite the equation as .
Step 2
Simplify .
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Step 2.1
Multiply by .
Step 2.2
Combine fractions.
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Step 2.2.1
Multiply by .
Step 2.2.2
Expand the denominator using the FOIL method.
Step 2.2.3
Simplify.
Step 2.3
Simplify the numerator.
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Step 2.3.1
Raise to the power of .
Step 2.3.2
Raise to the power of .
Step 2.3.3
Use the power rule to combine exponents.
Step 2.3.4
Add and .
Step 2.4
Rewrite as .
Step 2.5
Expand using the FOIL Method.
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Step 2.5.1
Apply the distributive property.
Step 2.5.2
Apply the distributive property.
Step 2.5.3
Apply the distributive property.
Step 2.6
Simplify and combine like terms.
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Step 2.6.1
Simplify each term.
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Step 2.6.1.1
Combine using the product rule for radicals.
Step 2.6.1.2
Multiply by .
Step 2.6.1.3
Rewrite as .
Step 2.6.1.4
Pull terms out from under the radical, assuming positive real numbers.
Step 2.6.1.5
Multiply .
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Step 2.6.1.5.1
Combine using the product rule for radicals.
Step 2.6.1.5.2
Multiply by .
Step 2.6.1.6
Multiply .
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Step 2.6.1.6.1
Combine using the product rule for radicals.
Step 2.6.1.6.2
Multiply by .
Step 2.6.1.7
Multiply .
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Step 2.6.1.7.1
Multiply by .
Step 2.6.1.7.2
Multiply by .
Step 2.6.1.7.3
Raise to the power of .
Step 2.6.1.7.4
Raise to the power of .
Step 2.6.1.7.5
Use the power rule to combine exponents.
Step 2.6.1.7.6
Add and .
Step 2.6.1.8
Rewrite as .
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Step 2.6.1.8.1
Use to rewrite as .
Step 2.6.1.8.2
Apply the power rule and multiply exponents, .
Step 2.6.1.8.3
Combine and .
Step 2.6.1.8.4
Cancel the common factor of .
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Step 2.6.1.8.4.1
Cancel the common factor.
Step 2.6.1.8.4.2
Rewrite the expression.
Step 2.6.1.8.5
Evaluate the exponent.
Step 2.6.2
Add and .
Step 2.6.3
Subtract from .
Step 2.7
Cancel the common factor of and .
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Step 2.7.1
Factor out of .
Step 2.7.2
Factor out of .
Step 2.7.3
Factor out of .
Step 2.7.4
Cancel the common factors.
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Step 2.7.4.1
Factor out of .
Step 2.7.4.2
Cancel the common factor.
Step 2.7.4.3
Rewrite the expression.
Step 3
Add to both sides of the equation.