Question

How do you solve `\frac { x } { x - 2} + 3= \frac { 2} { x - 2}`?

Answer 1

Not valid solution is possible for this equation.

Explanation:

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

`rArr x/(x-2)-2/(x-2)=-3`

`rArr (x-2)/(x-2)=-3`

`rArr 1 = -3color(white)("XXX")` Which is clearly impossible.

Answer 2

There is no solution. Please see the explanation.

Explanation:

A restriction, to prevent division by zero, must be added:

`x/(x -2) + 3 = 2/(x - 2);x!=2`

Now, we can multiply both sides by `x -2`, because we know that we are not multiplying by a conditional zero:

`x + 3(x -2) = 2;x!=2`

Distribute the 3:

`x + 3x -6 = 2;x!=2`

Combine like terms:

`4x = 8;x!=2`

`x = 2; x!=2`

This means that there is no solution to the equation.