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If \(\left(x+\dfrac{1}{x}\right):\left(x-\dfrac{1}{x}\right)=5:4\) then find the value of x.

 Jul 4, 2020
 #1
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( x + 1/x ) / ( x - 1/x )  =  5 / 4

 

Cross-multiply:       4( x + 1/x )  =  5(x - 1/x )

                                  4x + 4 / x  =  5x - 5/x

Multiply by x:                4x2 + 4  =  5x2 - 5

Add 5:                           4x2 + 9  =  5x2 

Subtract 4x2:                          9  =  x2

 

Two possible answers:  3  and  -3

If you place these numbers back into the original equation, you will find that 3 works and that -3 doesn't work.

 Jul 4, 2020

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