Question

x-1/x-2+x-3/x-4=3 1/3 solve for x by factorization method

Answer 1

x-1/x-2+x-3+x-4 =3 1/3
x-1/3x-9 = 10/3
x-1/3(x-3) =10/3
x-1/x-3 = 10
x-1= 10(x-3)
x-1 = 10x-30
10x-x = 30-1
9x= 29
x = 29/9

Answer 2

Answer: x= 3 and 2/3

Step-by-step explanation:

given that

$x-\frac{1}{x}+x-\frac{3}{x}-4=3\tfrac{1}{3}\\\\2x-\frac{4}{x}=\frac{10}{3}+4\\\\\frac{2x^{2}-4}{x}=\frac{22}{3}\\\\6x^{2}-22x-12=0\\\\(x-3)(6x-4) =0$

so x= 3 and x= 2/3