Evaluate
14-7\sqrt{3}\approx 1.875644347
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\frac{7\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}
Rationalize the denominator of \frac{7}{2+\sqrt{3}} by multiplying numerator and denominator by 2-\sqrt{3}.
\frac{7\left(2-\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{7\left(2-\sqrt{3}\right)}{4-3}
Square 2. Square \sqrt{3}.
\frac{7\left(2-\sqrt{3}\right)}{1}
Subtract 3 from 4 to get 1.
7\left(2-\sqrt{3}\right)
Anything divided by one gives itself.
14-7\sqrt{3}
Use the distributive property to multiply 7 by 2-\sqrt{3}.
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