Simplify 5 over 2+√ 3
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5/2+√3
=5×(2-√3)/(2+√3)(2-√3) (multiplying numerator and denominator by 2-√3)
=(10-5√3)/{(2)^2-(√3)^2}{since a^2-b^2=(a+b)(a-b)}
=(10-5√3)/(4-3)
=(10-5√3)/1
=10-5√3
=5×(2-√3)/(2+√3)(2-√3) (multiplying numerator and denominator by 2-√3)
=(10-5√3)/{(2)^2-(√3)^2}{since a^2-b^2=(a+b)(a-b)}
=(10-5√3)/(4-3)
=(10-5√3)/1
=10-5√3
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