Simplify: (\frac{2+\sqrt3}{2-\sqrt3}+\frac{2-\sqrt3}{2+\sqrt3}+\frac{\sqrt3-1}{\sqrt3+1})

Powers and Roots Practice Test 5

Question : 8 of 31

Marks: +1, -0

Simplify:

({2+√3}/{2-√3}+{2-√3}/{2+√3}+{√3-1}/{√3+1})

Solution:

({2+√3}/{2-√3}+{2-√3}/{2+√3}+{√3-1}/{√3+1})

= {({2+√3})^2 +({2-√3})^2}/{({2-√3})({2+√3})} +{√3-1}/{√3+1} ×{√3-1}/{√3-1}

={4+3+2√3+4+3-2√3}/{4-3}+(√3-1)^2/{(√3+1)(√3-1)}

=14/1+{2(2-√3)}/2

=14+2-√3=16-√3

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