# Simplify (5+ square root of 5)/(2- square root of 7)

5+52-7
Multiply 5+52-7 by 2+72+7.
5+52-7⋅2+72+7
Combine fractions.
Multiply 5+52-7 and 2+72+7.
(5+5)(2+7)(2-7)(2+7)
Expand the denominator using the FOIL method.
(5+5)(2+7)4+27-27-72
Simplify.
(5+5)(2+7)-3
(5+5)(2+7)-3
Expand (5+5)(2+7) using the FOIL Method.
Apply the distributive property.
5(2+7)+5(2+7)-3
Apply the distributive property.
5⋅2+57+5(2+7)-3
Apply the distributive property.
5⋅2+57+5⋅2+57-3
5⋅2+57+5⋅2+57-3
Simplify terms.
Simplify each term.
Multiply 5 by 2.
10+57+5⋅2+57-3
Move 2 to the left of 5.
10+57+2⋅5+57-3
Combine using the product rule for radicals.
10+57+25+5⋅7-3
Multiply 5 by 7.
10+57+25+35-3
10+57+25+35-3
Move the negative in front of the fraction.
-10+57+25+353
-10+57+25+353
The result can be shown in multiple forms.
Exact Form:
-10+57+25+353
Decimal Form:
-11.20565743…
Simplify (5+ square root of 5)/(2- square root of 7)

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