Question

find the value of x
1+1/2+1/3+1/x = 43/30​

Answer 1

Step-by-step explanation:

We have,

$1 + \frac{1}{2 + \frac{1}{3 + \frac{1}{x} } } = \frac{43}{30 }$

$\implies 1 + \frac{1}{2 + \frac{x}{ 3x + 1} } = \frac{43}{30 }$

$\implies 1 + \frac{1}{ \frac{7x + 2}{ 3x + 1} } = \frac{43}{30 }$

$\implies 1 + \frac{3x + 1}{ 7x + 2} = \frac{43}{30 }$

$\implies \frac{10x + 3}{ 7x + 2} = \frac{43}{30 }$

$\implies300x + 90 = 301x + 86$

$\implies x = 4$