Question

How do you solve `1/(c-2) + 1/c = 2/(c(c-2))`?

Answer 1

I found no real value of `c`.

Explanation:

I would choose `c(c-2)` as common denominator and write:
`(c+c-2)/(c(c-2))=2/(c(c-2))`
where on the left I arranged the numerators to the new common denominator.

So you can now simplify the two denominators:

`(c+c-2)/cancel((c(c-2)))=2/cancel((c(c-2)))`
`2c-2=2`
`2c=4`
`c=4/2=2`
BUT
if you use `c=2` into your original equation you get a division by zero that cannot be evaluated.