Question

x ≠ 0, 1, 2
Solve the following -
$\frac{1}{x - 2} + \frac{2}{x - 2} = \frac{6}{x}$
​

Answer 1

Method 1

1/x-2 +1/x-2 =6/x

Let, x-2 be a.

Therefore,

1/a+2/a=6/x

or, a+2a/a=6/x

or, ax+2ax=6a

or, 3ax =6a

or, x = 6a/3a

or, x = 2

Method 2

1/x-2 +1/x-2 =6/x

or, x-2+2(x-2)/x-2 =6/x

or, x²-2x+2x²-4x=6x-12

or, 3x²-6x-6x+12=0

or,. 3x²-12x+12=0

or. x²-4x+4=0

or,. x²-(2+2)x+4=0

or,. x²-2x-2x+4=0

or. x(x-2)-2(x-2)=0

or,. (x-2)(x-2)=0

Either,x-2=0 or,x-2=0

x=2 x=2

Hope it helps :)