Question

if x=1÷x-5 and x is not equal to 5find x^2-1÷x^2

Answer 1

$x = \frac{1}{x} - 5 \\ or. \: x - \frac{1}{x} = - 5 \\ or. \: (x + \frac{1}{ x } )^{2} = {(x - \frac{1}{x} )}^{2} + 4x \frac{1}{x} \\ or. \: x + \frac{1}{x} = \sqrt{ {( - 5 )}^{2} + 4 }= \sqrt{29} \\ \\ thus.. {x}^{2} - \frac{1}{ {x}^{2} } = (x - \frac{1}{x} )(x + \frac{1}{ x} ) \\ = - 5 \times \sqrt{29} = - 5 \sqrt{29}$
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