x-3/x-10 = x+1/2x-1 EMERGENCY!?

Presentation dodgy !

Assume that you mean , NOT as given , but as :-

(x - 3) / (x - 10) = (x + 1) / (2x - 1)

(x - 3)(2x - 1) = (x + 1)(x - 10)

2x² - 7x + 3 = x² - 9x - 10

x² + 2x + 13 = 0

x = [ - 2 ± √ (4 - 52) ] / 2

x = [ - 2 ± √ (- 48) ] / 2

x = [ - 2 ± i 4√3 ] / 2

x = - 1 ± i 2√3

(x - 3)/(x - 10) = (x + 1)/(2x - 1)
x - 3 = (x - 10)(x + 1)/(2x - 1)
(x - 3)(2x - 1) = x*x - 10*x + x*1 - 10*1
2x^2 - 6x - x + 3 = x^2 - 10x + x - 10
2x^2 - 7x + 3 = x^2 - 9x - 10
2x^2 - x^2 - 7x + 9x + 3 + 10 = 0
x^2 + 2x + 13 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = 2
c = 13

x = [-2 ±√(4 - 52)]/2
x = [-2 ±√-48]/2
x = -1 ±(i√48)/2

∴ x = -1 ±(i√48)/2

I believe the answer you seek is 2.499, that that you be by moving the 10 to the left side to make x-3/x=x+1/2x+9, then you have to move the lone xs, to make 3/x=1/2x+9, then you have to multiply across by 1/3 ( the reciprocal) of 3/1x, which gives you x=1/6x+3, 5/6x=3, x=2.4999