Question

Solve by factorisation
x+$\frac{1}{x}$=2.5

Answer 1

x^2 + 1 - 2.5 x = 0

2 x^2 - 5 x + 2 = 0 

2 x^2 - 4 x  - x + 2 = 0

2 x (x - 2)  - (x - 2) = 0

(2x - 1) (x -2 ) = 0

x = 1/2    or   2

Answer 2

By taking L.C.M.

x² + 1 = 2.5x
x² - 2.5x + 1 = 0

Multiplying both side by 2.

2x² - 5x + 2 = 0
2x² - 4x - x + 2 = 0

2x( x - 2 ) -1 ( x - 2 ) = 0

(2x - 1)(x - 2) = 0
x = 1/2          , x = 2