Question

solve the problem with solution get fast​

Answer 1

Answer:

The correct answer is option (iii) .

Step-by-step explanation:

$\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3-\dfrac{1}{3}}}}=\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{\dfrac{9-1}{3}}}}=\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{\dfrac{8}{3}}}}\\\\=\dfrac{1}{3+\dfrac{1}{3+\dfrac{3}{8}}}=\dfrac{1}{3+\dfrac{1}{\dfrac{24+3}{8}}}=\dfrac{1}{3+\dfrac{1}{\dfrac{27}{8}}}=\dfrac{1}{3+\dfrac{8}{27}}\\\\=\dfrac{1}{\dfrac{81+8}{27}}=\dfrac{1}{\dfrac{89}{27}}=\dfrac{27}{89}$

Note: Start simplifying from the end