Question

solve x/x-2+3x/x-4=32-2x/x^2-6x+8

Answer 1

plz

Answer 2

\[\frac{x}{x-2}+\frac{3x}{x-4}=\frac{32-2x}{x^2-6x+8}\] like that ?

Answer 3

x^2 -6x +8=(x-2)(x-4)

x(x-4) +3x(x-2) 2(16-x)
-------------- = ---------- - so restrictions will be : x not can being 2 and 4
(x-2)(x-4) (x-2)(x-4) because than these fractions are undefined

x^2 -4x +3x^2 -6x 32 -2x
----------------- = ---------
(x-2)(x-4) (x-2)(x-4)

4x^2 -10x 32 -2x
---------- = ---------
(x-2)(x-4) (x-2)(x-4)

4x^2 -10x =32 -2x
4x^2 -8x -32=0
4(x^2 -4x -8)=0
x^2 -4x -8=0

x_1,2=(4+/- sqrt(16+32))/2 =(4+/- 4sqrt3)/2 = 2+/- 2sqrt3