Given that: \(\frac{1}{{1 + \frac{1}{{1 + \frac{1}{{1 + \frac{1}{x}}}}}}} = \frac{5}{8}\) then what is the value of x?
2
Simplify the nested fraction from inside out:
\[1+\tfrac{1}{x}=\tfrac{x+1}{x};\quad 1+\tfrac{x}{x+1}=\tfrac{2x+1}{x+1};\quad 1+\tfrac{x+1}{2x+1}=\tfrac{3x+2}{2x+1}\]
So the LHS equals \(\dfrac{2x+1}{3x+2}=\dfrac{5}{8}\). Cross-multiplying:
\[8(2x+1)=5(3x+2)\Rightarrow 16x+8=15x+10\Rightarrow x=\mathbf{2}\]
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Important Questions from Linear Equation in 1 Variable
A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?
The sum of three consecutive number is 126. Find the highest number?
Simplify 5x(x + 2) + 4x
A.5x 2+ 10
B.9x + 10
C.5x 2- 14x
D.5x 2+ 14xSolve:
x - 4 = -3
A. 7
B. -1
C. -7
D. 1
If 4(3x - 2) = 2(3x + 8), Then x = ?
A. 1
B. 2
C. 3
D. 4
