Question

slove for x,( 1/x-2)+(2/x-1)=6/x​

Answer 1

Answer:

3, 4/3

Step-by-step explanation:

$\frac{1}{x-2}+\frac{2}{x-1}=\frac{6}{x}$

$\rightarrow \frac{x-1+2x-4}{(x-2)(x-1)}=\frac{6}{x}$

$\rightarrow \frac{3x-5}{x^2-3x+2}=\frac{6}{x}$

$\rightarrow x(3x-5)=(x^2-3x+2)6$

$\rightarrow 3x^2-5x= 6x^2-18x+12$

$\rightarrow 3x^2-13x+12=0$

$\rightarrow 3x^2-4x-9x+12=0$

$\rightarrow x(3x-4)-3(3x+4)=0$

$\rightarrow (x-3)(3x-4)=0$

so, x-3 = 0  or, 3x-4 = 0

x = 3, 4/3