Question

How do you solve `\frac { x - 2} { x ^ { 2} - 4} + \frac { x } { x - 2} = \frac { 1} { x + 2}`?

Answer 1

`x=0`

Explanation:

Given:

`(x-2)/(x^2-4)+x/(x-2) = 1/(x+2)`

Note that:

`(x-2)/(x^2-4) = color(red)(cancel(color(black)((x-2))))/(color(red)(cancel(color(black)((x-2))))(x+2)) = 1/(x+2)`

with exclusion `x != 2`

So the given equation simplifies to:

`1/(x+2) + x/(x-2) = 1/(x+2)`

Subtract `1/(x+2)` from both sides to get:

`x/(x-2) = 0`

Multiply both sides by `(x-2)` to get:

`x = 0`

So this is the only solution.