if x = 1/x-5 then find x - 1/x
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Step-by-step explanation:
x=1/(x-5)
Or x-5=1/x since x is not equal to zero
Or x-1/x=5 ………(1)
Squaring both sides
(x-1/x)^2=25
Or x^2–2×x×(1/x)+1/(x^2)=25
Or x^2–2+1/(x^2)=25
Or x^2+1/(x^2)=25+2=27
Adding 2 to both sides we have
x^2+2+1/(x^2)=29
Or x^2+2×x×(1/x)+1/(x^2)=29
Or (x+1/x)^2=29
Or x+1/x=+-(29)^(1/2)………(2)
Multiplying (1) and (2) we have
x^2–1/x^2=+-5×(29)^(1/2)
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