Question

$if \\\\\frac{x^2-1}{x} = \frac{5}{2}\\\\ find \\\\ \frac{x-1}{x} and \frac{x^3-1}{x^3}$

Answer 1

Answer:

$\frac{ {x}^{2} + 1}{x} = \frac{5}{2} \\ cross \: multiply \\ 2( {x}^{2} + 1) = 5x \\ 2 {x}^{2} + 2 = 5x \\ 2 {x}^{2} - 5x + 2 = 0 \\ 2 {x}^{2} - 4x - x + 2 = 0 \\ (2 {x}^{2} - 4x) - (x + 2) = 0 \\ 2x(x - 2) - 1(x - 2) = 0 \\ (x - 2)(2x - 1) = 0 \\ (x - 2 = 0)(2x - 1 = 0) \\ x = 2 \: and \: x = \frac{1}{2} \\ Therefore, \: x= 2 \\ \frac{x - 1}{x} = \frac{2 - 1}{2} = \frac{1}{2} \\ \frac{ {x}^{3} - 1 }{ {x}^{3} } = \frac{8 - 1}{8} = \frac{7}{8}$

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