Question

How do you solve `6/(n+3) + 20/(n^2+n-6) = 5/(n-2)`?

Answer 1

The Least Common Denominator of the terms in the given equation is
`color(white)("XXXX")` `(n^2+n-6) = (n+3)(n-3)`

So the given equation could be written:
`color(white)("XXXX")` `(6(n-2)+20)/(n^2+n-6) = (5(n+3))/(n^2+n-6)`

and assuming `n!=-3` and `n!=2`
(otherwise terms of the original equation would be undefined).

`color(white)("XXXX")` `6(n-2) + 20 = 5(n+3)`

`color(white)("XXXX")`n = 7#