2x +3x-2Solve for xr+ x-2 2x3

1.	2x +3x-2Solve for xr+ x-2 2x3
Answer» x + 1 / x - 1 + x - 2 / x + 2 = 4 - 2x + 3 / x - 2 Taking lcm we get (x + 2)(x + 1) + (x - 1)(x - 2) / (x -1) ( x + 2) = 4(x - 2) - (2 x + 3) / x - 2 x^2 + 3x + 2 + x^2 - x - 2x + 2 / x^2 + x - 2 = 2x - 11 / x - 2 = 2x - 11 / x - 2 2x^2 + 4 / x^2 + x - 2 = 2x - 11 / x - 2 2x^3 - 4x^2 + 4x - 8 = 2x^3 + 2x ^2 - 4x - 11x^2 - 11x + 22 5x^2 + 19x - 30 = 0 5x^2 + 25x - 6x - 30 = 0 5x( x + 5) - 6( x + 5) = 0 (x + 5)( 5 x - 6) = 0 x + 5 = 0, 5 x + 6 = 0 x = - 5 , x = 6 / 5

Answer»

x + 1 / x - 1 + x - 2 / x + 2 = 4 - 2x + 3 / x - 2

Taking lcm we get

(x + 2)(x + 1) + (x - 1)(x - 2) / (x -1) ( x + 2) = 4(x - 2) - (2 x + 3) / x - 2

x^2 + 3x + 2 + x^2 - x - 2x + 2 / x^2 + x - 2 = 2x - 11 / x - 2 = 2x - 11 / x - 2

2x^2 + 4 / x^2 + x - 2 = 2x - 11 / x - 2

2x^3 - 4x^2 + 4x - 8 = 2x^3 + 2x ^2 - 4x - 11x^2 - 11x + 22

5x^2 + 19x - 30 = 0

5x^2 + 25x - 6x - 30 = 0

5x( x + 5) - 6( x + 5) = 0

(x + 5)( 5 x - 6) = 0

x + 5 = 0, 5 x + 6 = 0

x = - 5 , x = 6 / 5

Discussion