7-4√3÷7+4√3

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Solution

By taking the conjugate of 7+4root(3) which is equal to 7-4root(3) and multiplying numerator and denominator
we write
[7-4root(3)][7-4root(3)]/[7+4root(3)][7-4root(3)]
(a-b)^2=a^2-2ab+b^2
therefore numerattor is
7^2-274root(3)+(4root(3))^2
=49-56root(3)+163
=49-56root(3)+48
=97-56root(3) is the numerator.
now denominator is of the form
(a+b)(a-b)=a^2-b^2
therefore

denominator=7^2-(4root(3))^2
=49-48
=1.
so the answer for the que is
numerator/denominator
=97-56root(3)/1
=97-56root(3)

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