Question

(x-1/x-2)+(x-3/x-4) = 3*1/3

Answer 1

Step-by-step explanation:

x-1 x-2 +1 1

___ = _____ = 1 + ___

x-2 x-2 x-2

x-3 x-4 +1 1

___ = _____ = 1+ ___

x-4 x-4 x-4

given equation can be written as

1+ 1/(x-2) +1 + 1/(x-4) = 3 +1/3

1/(x-2)+1/(x-4) = 3-2 +1/3 = 1 +1/3 = 4/3

x-2+x-4/(x-2)(x-4) = 4/3

2x-6/(x-2)(x-4) =4/3

3(x-3)=2(x-2)(x-4)

3x-9 = 2(x²-6x+8) =2x²-12x+16

2x²-15x+25 =0

2x²-10x-5x+25=0

2x(x-5)-5(x-5)=0

(2x-5)(x-5) =0

x=5/2, 5