If \(\left(x+\dfrac{1}{x}\right):\left(x-\dfrac{1}{x}\right)=5:4\) then find the value of x.
+23245 ( 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.
