Question

What is the solution of this ? `x/(x-2) + 3=2/(x-2)`

Answer 1

x =2 is the algebraic answer to the equation but the algebraic answer is not allowed so there is no rational solution.

Explanation:

the solution is to multiply everything by (x -2) to remove the denominators and eliminate the fractional forms of the terms.

`(x-2) xx { (x)/(x-2)} + (x-2) xx 3 = {(x-2) xx {(2)/(x-2)}`

Multiplying everything (x-2) results in

`x + 3x -6 = 2`

Combine the x terms and add six to both sides

`x + 3x -6 + 6 = 2 +6` This gives

`4x = 8`

Divide both sides by 4

`(4x)/4 = 8/4` the answer is

`x = 2`

However (x-2) when x = 2 give # 2-2 = 0

Putting this into the equation gives

`2/(2-2) +3 = 2/(2-2)`

which gives

`2/0 + 3 = 2/0` dividing by zero is undefined

this means that the only algebraic answer is undefined and is not allowed.