# Solve for a ( square root of 11+ square root of 7)/( square root of 11- square root of 7)=a+b square root of 7

Rewrite the equation as .
Simplify .
Multiply by .
Combine fractions.
Multiply and .
Expand the denominator using the FOIL method.
Simplify.
Simplify the numerator.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Combine using the product rule for radicals.
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Combine using the product rule for radicals.
Multiply by .
Combine using the product rule for radicals.
Multiply by .
Combine using the product rule for radicals.
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Cancel the common factor of and .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Subtract from both sides of the equation.
Solve for a ( square root of 11+ square root of 7)/( square root of 11- square root of 7)=a+b square root of 7

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