Simplify- 11-231-23-8-91-23

The correct option is A 13/15 1/1+2/31+23+8/9/1 23 ⇒1/1+2/31+23+8/9/1/3 ⇒1/1+2/31+23+8/3 ⇒1/1+2/313/3 ⇒1/1+213 ⇒1/15/13 ...

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Byju's Answer

Standard X

Mathematics

Componendo and Dividendo

Simplify: 1...

Question

Simplify: $\frac{1}{1 + \frac{\frac{2}{3}}{1 + \frac{2}{3} + \frac{\frac{8}{9}}{1 - \frac{2}{3}}}}$

\frac{11}{13}

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\frac{13}{15}

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\frac{13}{11}

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\frac{15}{13}

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Solution

The correct option is A $\frac{13}{15}$
$\frac{1}{1 + \frac{\frac{2}{3}}{1 + \frac{2}{3} + \frac{\frac{8}{9}}{1 - \frac{2}{3}}}}$
$\Rightarrow \frac{1}{1 + \frac{\frac{2}{3}}{1 + \frac{2}{3} + \frac{\frac{8}{9}}{\frac{1}{3}}}}$
$\Rightarrow \frac{1}{1 + \frac{\frac{2}{3}}{1 + \frac{2}{3} + \frac{8}{3}}}$
$\Rightarrow \frac{1}{1 + \frac{\frac{2}{3}}{\frac{13}{3}}}$
$\Rightarrow \frac{1}{1 + \frac{2}{13}}$
$\Rightarrow \frac{1}{\frac{15}{13}}$
$\Rightarrow \frac{13}{15}$

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Similar questions

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$