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Question Number 207247 by hardmath last updated on 10/May/24

$$8+\frac{18}{2+\frac{7}{5+\frac{2}{\mathbf{x}}}}=14\mathrm{find}:\mathbf{x}=?$$

Commented by Frix last updated on 10/May/24

$$x=1$$

Answered by Rasheed.Sindhi last updated on 11/May/24

$$8+\frac{18}{2+\frac{7}{5+\frac{2}{\mathbf{x}}}}=14\mathrm{find}:\mathbf{x}=?$$$$\Rightarrow \frac{18}{2+\frac{7}{5+\frac{2}{\mathbf{x}}}}=6$$$$\Rightarrow \frac{3}{2+\frac{7}{\frac{5x+2}{\mathbf{x}}}}=1$$$$\Rightarrow \frac{3}{2+\frac{7x}{5x+2}}=1$$$$\Rightarrow \frac{3}{\frac{10x+4+7x}{5x+2}}=1$$$$\Rightarrow \frac{3(5x+2)}{17x+4}=1$$$$\Rightarrow 15x+6=17x+4$$$$\Rightarrow 2x=2\Rightarrow x=1$$

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