Question

x:(3x+1/x-2) -10(x-2/3x+1)=3 ; [x not equal to 0,-1/3] solve this

Answer 1

$\frac{3x + 1}{x - 2} - 10( \frac{x - 2}{3x + 1} ) = 3 \\ => \frac{3x + 1}{x - 2} - 10 \times \frac{x - 2}{3x + 1} = 3 \\ = > \frac{ {(3x + 1)}^{2} - 10 \times {(x - 2)}^{2} }{(x - 2)(3x + 1)} = 3 \\ = > \frac{9 {x}^{2} + 6x + 1 - 10( {x}^{2} - 4x + 4) }{3 {x}^{2} + x - 6x - 2 } = 3 \\ = > \frac{9 {x}^{2} + 6x + 1 - 10 {x}^{2} + 40x - 40}{3 {x}^{2} - 5x - 2 } = 3 \\ = > - {x}^{2} + 46x - 39 = 3(3 {x}^{2} - 5x - 2) \\ = > - {x}^{2} + 46x - 39 = 9 {x}^{2} - 15x - 6 \\ = > - {x}^{2} - 9 {x}^{2} + 46 x+ 15x - 39 + 6 = 0 \\ = > 10 {x}^{2} + 61x - 33 = 0 \\ = > 10 {x}^{2} - 61x + 33 = 0$

=> 10x^2 - 6x - 55x +33 = 0

=> 2x( 5x-3) - 11( 5x -3) =0

=> (2x-11)(5x-3)=0

so

2x-11=0

2x = 11

x = 11/2

or

5x-3=0

5x = 3

x = 5/3